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BEGIN:VEVENT
SUMMARY:Marija Galic (Univerzity of Zagreb)
DTSTART:20201006T070000Z
DTEND:20201006T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/5
DESCRIPTION:Title: Existence of a weak solution to a 3d nonlinear\, moving boundary
FSI problem\nby Marija Galic (Univerzity of Zagreb) as part of Necas
PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna
25\,Prague.\n\nAbstract\nWe consider a nonlinear\, moving boundary\, flui
d-structure interaction problem\nbetween an incompressible\, viscous fluid
flow\, and an elastic structure composed\nof a cylindrical shell supporte
d by a mesh-like elastic structure. The\nfluid flow is modeled by the time
-dependent Navier-Stokes equations in a threedimensional\ncylindrical doma
in\, while the cylindrical shell is described by the\ntwo-dimensional line
arly elastic Koiter shell equations allowing displacements\nin all three s
patial directions. The mesh-like structure is modeled as a onedimensional\
nhyperbolic net made of linearly elastic curved rods. The fluid and\nthe m
esh-supported structure are coupled via the kinematic and dynamic boundary
\ncoupling conditions describing continuity of velocity and balance of con
tact\nforces at the fluid-structure interface. We prove the existence of a
weak solution\nto this nonlinear\, moving boundary problem by using the t
ime-discretization\nvia Lie operator splitting method\, Arbitrary Lagrangi
an-Eulerian mapping and\nnon-trivial compactness result. This is a joint w
ork with Suncica Canic and \nBoris Muha.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralph Chill (Technical University of Dresden)
DTSTART:20201013T065000Z
DTEND:20201013T082000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/6
DESCRIPTION:Title: Degenerate gradient systems: the bidomain problem and Dirichlet-
to-Neumann operators\nby Ralph Chill (Technical University of Dresden)
as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of
Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe identify a common structure
behind several parabolic PDE\nmodels involving\nDirichlet-to-Neumann oper
ators\, the bidomain operator\, and some more\,\nand we show that\nthey ac
tually have a gradient structure\, possibly up to lower order\nperturbatio
ns. This has\nconsequences for wellposedness of these PDEs\, regularity of
solutions\nand their asymptotic\nbehaviour.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Sperone (Faculty of Mathematics and Physics\, Charles Un
iversity in Prague)
DTSTART:20201020T065000Z
DTEND:20201020T082000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/7
DESCRIPTION:Title: Explicit bounds for the generation of a lift force exerted by st
eady-state Navier-Stokes flows over a fixed obstacle\nby Gianmarco Spe
rone (Faculty of Mathematics and Physics\, Charles University in Prague) a
s part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Ma
thematics\,Zitna 25\,Prague.\n\nAbstract\nWe analyze the steady motion of
a viscous incompressible fluid\nin a two- and three-dimensional channel co
ntaining an obstacle through\nthe Navier-Stokes equations under different
types of boundary\nconditions. In the 2D case we take constant non-homogen
eous Dirichlet\nboundary data in a (virtual) square containing the obstacl
e\, and\nemphasize the connection between the appearance of lift and the u
nique\nsolvability of Navier-Stokes equations. In the 3D case we consider
mixed\nboundary conditions: the inflow is given by a fairly general datum
and\nthe flow is assumed to satisfy a constant traction boundary condition
on\nthe outlet. In the absence of external forcing\, explicit bounds on t
he\ninflow velocity guaranteeing existence and uniqueness of such steady\n
motion are provided after estimating some Sobolev embedding constants\nand
constructing a suitable solenoidal extension of the inlet velocity.\nIn t
he 3D case\, this solenoidal extension is built through the Bogovskii\nope
rator and explicit bounds on its Dirichlet norm (in terms of the\ngeometri
c parameters of the obstacle) are found by solving a variational\nproblem
involving the infinity-Laplacian.\nThe talk accounts for results obtained
in collaboration with Filippo\nGazzola and Ilaria Fragalà (both at Polite
cnico di Milano).\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Piasecki (Univerzity of Warsaw)
DTSTART:20201103T075000Z
DTEND:20201103T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/8
DESCRIPTION:Title: A maximal regularity approach to compressible mixtures\nby T
omasz Piasecki (Univerzity of Warsaw) as part of Necas PDE seminar\n\nLect
ure held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbs
tract\nI will present recent results obtained in collaboration with Yoshih
iro\nShibata and Ewelina Zatorska. We investigate the well posedness of a\
nsystem describing flow of a mixture of compressible constituents.\nThe sy
stem in composed of Navier-Stokes equations coupled with equations\ndescri
bing balance of fractional masses. A crucial property is that the\nsystem
is non-symmetric and only degenerate parabolic.\nHowever\, it reveals a st
ructure which allows to transform it to a\nsymmetric parabolic problem usi
ng appropriate change of unknowns. In order\nto treat the transformed prob
lem we write it in Lagrangian coordinates and\nlinearize.\nFor the related
linear problem we show a Lp-Lq maximal regularity estimate\napplying the
theory of R-bounded solution operators. This estimate allows\nto show loca
l existence and uniqueness. Next\, assuming additionally\nboundedness of t
he domain we extend the maximal regularity estimate and\nshow exponential
decay property for the linear problem. This allow us to\nshow global well
-posedness of the original problem for small data.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Bravin (Basque Center for Applied Mathematics)
DTSTART:20201124T075000Z
DTEND:20201124T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/9
DESCRIPTION:Title: Interaction of a small rigid body with fluids\nby Marco Brav
in (Basque Center for Applied Mathematics) as part of Necas PDE seminar\n
\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\
n\nAbstract\nIn this talk I will present a recent result in collaboration
with Prof Necasova\, where we study the interaction between a small rigid
body and a compressible viscous fluid modeled by the compressible Navier-S
tokes equations.\n\nIn particular I will recall the previous results where
the fluids were supposedly incompressible and then I will focus my attent
ion on the improved pressure estimates that are the main novelty in our re
sult. In contrast with the incompressible case the pressure estimates depe
nd on a lower bound of the mass and the inertia matrix of the object as it
s size tends to zero.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalousek (Institute of Mathematics\,CAS)
DTSTART:20201201T075000Z
DTEND:20201201T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/10
DESCRIPTION:Title: Global existence of weak solutions for a magnetic fluid model\nby Martin Kalousek (Institute of Mathematics\,CAS) as part of Necas PD
E seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 2
5\,Prague.\n\nAbstract\nThe talk is devoted to the presentation of recent
results that concern the global in time existence of weak solutions of a s
ystem of partial differential equations modeling a diffuse interface flow
of two Newtonian incompressible magnetic fluids. The system consists of th
e incompressible Navier-Stokes equations coupled with an evolutionary equa
tion for the magnetization vector and the Cahn-Hilliard equations. Present
ed results are based on the joint work with S. Mitra and A. Schlömerkempe
r.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tong Tang (University of Nanjing)
DTSTART:20201208T075000Z
DTEND:20201208T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/11
DESCRIPTION:Title: Global existence of weak solutions to the quantum Navier-Stokes
equations\nby Tong Tang (University of Nanjing) as part of Necas PDE
seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\
,Prague.\n\nAbstract\nIn this talk\, we proved the global existence of wea
k solutions to the\nquantum Navier-Stokes equations with non-monotone pres
sure. Motivated by\nthe work of Antonell-Spirito(2017\, Arch. Ration. Mech
. Anal.\, 1161-1199)\nand Ducomet-Necasova-Vasseur (2010\, Z. Angew. Math.
Phys.\, 479-491)\, we\nconstruct the suitable approximate system and obta
in the corresponding\ncompactness by B-D entropy estimate and Mellet-Vasse
ur inequality.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Danchin (University of Creteil)
DTSTART:20201215T075000Z
DTEND:20201215T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/12
DESCRIPTION:Title: A class of global relatively smooth solutions for the Euler-Poi
sson system\nby Raphael Danchin (University of Creteil) as part of Nec
as PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zi
tna 25\,Prague.\n\nAbstract\nIn this joint work with X. Blanc\, B. Ducomet
and Š.\nNečasová (to appear in JHDE)\, we construct a class of global
solutions\nto the Cauchy problem for the isentropic Euler equations couple
d with\nthe Poisson equation\, in the whole space. The initial density is
assumed\nto decay to 0 at infinity and the initial velocity is close to so
me\nreference velocity with Jacobian having positive spectrum bounded away
\nfrom 0. By a suitable adaptation of Grassin-Serre’s work on the\n`pure
’ compressible Euler equations\, we obtain a global smooth\nsolution th
e large time behavior of which may be described in terms of\nsome solution
of the multi-dimensional Burgers equation. The stability\nof some special
spherically symmetric stationary solution is also\ndiscussed.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Mucha (University of Warsaw)
DTSTART:20210105T075000Z
DTEND:20210105T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/13
DESCRIPTION:Title: Flows initiated by ripped densities\nby Piotr Mucha (Univer
sity of Warsaw) as part of Necas PDE seminar\n\nLecture held in Blue Hall\
, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe address the
question: Are solutions to the equations of\nviscous flows that are initia
ted by a density function given by a\ncharacteristic function of a set reg
ular and unique? The positive\nanswer is possible for the compressible Na
vier-Stokes equations if the\nbulk/volume viscosity is large. The limit ca
se of the homogeneous\nincompressible NSEs will be discussed too.\nThe tal
k will be based on results with Raphael Danchin:\nRD\, PBM: Compressible N
SEs with ripped density\, arXiv\;\nRD\, PBM: The incompressible NSEs in va
cuum\, CPAM2019.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART:20210126T075000Z
DTEND:20210126T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/14
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART:20210202T075000Z
DTEND:20210202T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/15
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART:20210209T075000Z
DTEND:20210209T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/16
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART:20210216T075000Z
DTEND:20210216T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/17
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART:20210223T075000Z
DTEND:20210223T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/18
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Coti Zelati (Imperial College London)
DTSTART:20210316T080000Z
DTEND:20210316T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/19
DESCRIPTION:Title: Stationary Euler flows near the Kolmogorov and Poiseuille flows
\nby Michele Coti Zelati (Imperial College London) as part of Necas PD
E seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 2
5\,Prague.\n\nAbstract\nWe exhibit a large family of new\, non-trivial sta
tionary\nstates of\nanalytic regularity\, that are arbitrarily close to th
e Kolmogorov flow\non the\nsquare torus. Our construction of these station
ary states builds on a\ndegeneracy in the global structure of the Kolmogor
ov flow. This is in\ncontrast\nwith both the Kolmogorov flow on a rectangu
lar torus and the\nPoiseuille flow\nin a channel\, for which we can show t
hat the only stationary states\nnear them\nmust be shears. This has surpri
sing consequences in the context of\ninviscid\ndamping in 2D Euler and enh
anced dissipation in Navier-Stokes.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Hofmanova (University of Bielefeld)
DTSTART:20210406T070000Z
DTEND:20210406T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/20
DESCRIPTION:Title: Non-uniqueness in law of stochastic 3D Navier--Stokes equations
\nby Martina Hofmanova (University of Bielefeld) as part of Necas PDE
seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\
,Prague.\n\nAbstract\nWe consider the stochastic Navier--Stokes equations
in three dimensions and prove that the law of analytically weak solutions
is not unique. In particular\, we focus on two iconic examples of a stoch
astic perturbation: either an additive or a linear multiplicative noise dr
iven by a Wiener process. In both cases\, we develop a stochastic counterp
art of the convex integration method introduced recently by Buckmaster an
d Vicol. This permits to construct probabilistically strong and analytical
ly weak solutions defined up to a suitable stopping time. In addition\, th
ese solutions fail the corresponding energy inequality at a prescribed tim
e with a prescribed probability. Then we introduce a general probabilistic
construction used to extend the convex integration solutions beyond the s
topping time and in particular to the whole time interval $[0\,\\infty)$.
Finally\, we show that their law is distinct from the law of solutions obt
ained by Galerkin approximation. In particular\, non-uniqueness in law hol
ds on an arbitrary time interval $[0\,T]$\, $T>0$.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fanelli (University of Lyon)
DTSTART:20210413T070000Z
DTEND:20210413T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/21
DESCRIPTION:Title: Statistical solutions to the barotropic Navier-Stokes equations
\nby Francesco Fanelli (University of Lyon) as part of Necas PDE semin
ar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prag
ue.\n\nAbstract\nIn this talk we are concerned with the notion of statisti
cal solutions to some models of fluid mechanics. We focus on the barotropi
c Navier-Stokes equations\, supplemented with non-homogeneous boundary dat
a.\nIn the first part of the talk\, we study dynamical properties of stati
stical solutions. Our approach\, different from the classical one of Foia
ş-Prodi and Vishik-Fursikov for the incompressible system\, is based on a
semiflow selection procedure. This allows us to define statistical soluti
on as the push-forward measure of the initial probability distribution on
the space of data of the Navier-Stokes system. We then investigate questio
ns like existence and stability of statistical solutions.\nIn the second p
art of the talk\, we focus on the special class of stationary statistical
solutions. In particular\, we explore their role in the investigation of t
he validity of the so-called ergodic hypothesis in the context of the baro
tropic Navier-Stokes equations.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Lannes (University of Bordeaux)
DTSTART:20210302T080000Z
DTEND:20210302T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/22
DESCRIPTION:Title: Some problems arising in wave-structure interactions\nby Da
vid Lannes (University of Bordeaux) as part of Necas PDE seminar\n\nLectur
e held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstr
act\nThere are different formulations of the water waves problem. One of\n
them is to formulate it as a system of equations coupling two\nquantities\
, e.g. the free surface elevation $\\zeta$ and the horizontal\ndischarge $
Q$. Actually\, one can understand the water waves problem as\na system on
three quantities\, $\\zeta$\, $Q$ and the surface pressure\n$P_s$ under th
e constraint that $P_s$ is constant (and therefore\ndisappears from the eq
uations).\nWhen we consider in addition a floating body then\, under the b
ody\, we\nstill have a system of equations on the same three quantities\,
but\nthis time the constraint is not on the pressure but on the surface of
\nthe water\, that must coincide with the bottom of the floating object.\n
Wave-structure interactions can be understood as the coupling of these\ntw
o different constrained problems. We shall briefly analyse this\ncoupling
and show among other things how it dictates the evolution of\nthe contact
line between the surface of the water and the surface of\nthe floating bod
y\, and how to transform it into transmission problems\nthat raise many ma
thematical issues such as fully nonlineary\nhyperbolic initial boundary va
lue problems\, dispersive boundary\nlayers\, initial boundary value proble
ms for nonlocal equations\, etc.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vaclav Macha (Institute of Mathematics\, Czech Academy of Sciences
)
DTSTART:20210309T080000Z
DTEND:20210309T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/23
DESCRIPTION:Title: Local-in-time existence of strong solutions to a class of compr
essible non-Newtonian Navier-Stokes equations\nby Vaclav Macha (Instit
ute of Mathematics\, Czech Academy of Sciences) as part of Necas PDE semin
ar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prag
ue.\n\nAbstract\nWe show a local-in-time existence of a strong solution to
the generalized compressible Navier-Stokes equation for arbitrarily large
initial data. The goal is reached by $L^p$-theory for linearized equation
s which are obtained with help of the Weis multiplier theorem. This work w
as done in collaboration with M. Kalousek and Š. Nečasová.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonin Novotny (University of Toulon)
DTSTART:20210323T073000Z
DTEND:20210323T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/24
DESCRIPTION:Title: Compressible fluids with nonhomogeneous boundary data I\nby
Antonin Novotny (University of Toulon) as part of Necas PDE seminar\n\nLe
cture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nA
bstract\nWe shall discuss several problems in the mathematical analysis of
viscous compressible\nfluids under the action of non zero inflow-outflow
boundary conditions.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonin Novotny (University of Toulon)
DTSTART:20210330T070000Z
DTEND:20210330T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/25
DESCRIPTION:Title: Compressible fluids with nonhomogeneous boundary data II\nb
y Antonin Novotny (University of Toulon) as part of Necas PDE seminar\n\nL
ecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\n
Abstract\nWe shall discuss several problems in the mathematical analysis o
f viscous compressible\nfluids under the action of non zero inflow-outflo
w boundary conditions.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University)
DTSTART:20210511T070000Z
DTEND:20210511T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/26
DESCRIPTION:Title: R-solver\, Maximal Regularity and Mathematical Fluid Dynamics\nby Yoshihiro Shibata (Waseda University) as part of Necas PDE seminar\
n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.
\n\nAbstract\nMaximal Regularity is an important tool to show the existenc
e of strong solutions of quasi-linear system of parabolic equations\, for
example free boundary problems for the Navier-Stokes equations. In this le
cture\, I will talk about a systematic approach for the Lp maximal regular
ity by using the R-solver. This approach is quite useful to control the hi
gh frequency part of solutions to the linearized problem\, and so we can p
rove the local well-posedness for the dynamical equations appearing in the
mathematical fluid dynamics. But\, to prove the global well-posedness at
least for small initial data\, we have to control the low frequency part.
To do this I use so called Lp-Lq decay estimate for the semigroup group as
sociated with the linearized problem\, like Stokes equations. In this talk
\, I will present how to prove the maximal regularity by using an R-solver
and how to control the low frequency part by using Lp-Lq estimates to pro
ve the global wellposedness in some concrete example\, like equations desc
ribing the compressible viscous fluid flow.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franc Merle (Université de Cergy-Pontoise)
DTSTART:20210518T070000Z
DTEND:20210518T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/27
DESCRIPTION:Title: On the implosion of a three dimensional compressible fluid\
nby Franc Merle (Université de Cergy-Pontoise) as part of Necas PDE semin
ar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prag
ue.\n\nAbstract\nWe\nconsider the compressible three dimensional Navier St
okes and Euler\nequations. In a suitable regime of barotropic laws\, we co
nstruct a set\nof finite energy smooth initial data for which the correspo
nding\nsolutions to both equations implode (with infinite density) at a la
ter\ntime at a point\, and completely describe the associated formation of
\nsingularity. Two essential steps of analysis are the existence of very\n
regular self-similar solutions to the\ncompressible Euler equations for qu
antized values of the speed and the\nderivation of spectral gap estimates
for the associated linearized flow\nwhich are addressed in the companion p
apers \\cite{MRRSprofile\,\nMRRSdefoc}. All blow up dynamics obtained for
the Navier-Stokes problem\nare of type II (non self-similar).\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ewelina Zatorska (Imperial College London)
DTSTART:20210525T080000Z
DTEND:20210525T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/28
DESCRIPTION:Title: Low Mach and low Froude numbers limit for the compressible Navi
er-Stokes equations with density-dependent viscosity coefficients\nby
Ewelina Zatorska (Imperial College London) as part of Necas PDE seminar\n\
nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n
\nAbstract\nIn this talk I will present a recent result on singular limit
for compressible Navier-Stokes equations involving low Mach and low Froude
numbers. We assume that the physical domain is the periodic box in three
space dimensions\, and that the limiting density profile is smooth\, separ
ated from zero and bounded from above. Derivation of the\, so-called\, ane
lastic approximation was proven previously by N. Masmoudi in 2007\, who us
ed as an approximation the barotropic compressible Navier-Stokes equations
with constant viscosity coefficients. In our result\, the approximate sys
tem includes the viscosity coefficients depending on the density and the s
ingular form of the pressure.\nThe result is based on a joint paper with F
rancesco Fanelli.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Maremonti (Università della Campania Luigi Vanvitelli)
DTSTART:20210504T070000Z
DTEND:20210504T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/29
DESCRIPTION:Title: On the uniqueness of a suitable weak solution to the Navier-Sto
kes Cauchy problem\nby Paolo Maremonti (Università della Campania Lui
gi Vanvitelli) as part of Necas PDE seminar\n\nLecture held in Blue Hall\,
Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe are dealing w
ith the Navier-Stokes Cauchy problem. We investigate some results of regul
arity and uniqueness related to suitable weak\nsolutions. The suitable wea
k solution notion is meant in the sense introduced by Caffarelli-Kohn-Nire
nberg. In paper [1]\, we recognize that a\nsuitable weak solution enjoys m
ore regularity than Leray-Hopf weak solutions\, that allows us to furnish
new uniqueness results for the solutions.\nActually\, we realize two resul
ts. The first one is a new sufficient condition on the initial datum u0 fo
r uniqueness. We work on existing suitable\nweak solution\, that is\, we d
o not construct a more regular weak solution\ncorresponding to our initial
datum. The second result employs a weaker\ncondition with respect to prev
ious ones (almost $u_0 \\in L^2$)\, but\, just for\none of the two compar
ed weak solutions\, we need a “special” Prodi-Serrin\ncondition. It is
“special” as it is local in space.\n\nReferences: [1] Crispo F. and M
aremonti P.\, On the uniqueness of a suitable weak solution\nto the Navier
-Stokes Cauchy problem\, SN Partial Differential Equations and\nApplicatio
ns\, to appear.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Flandoli (University of Pisa)
DTSTART:20210427T070000Z
DTEND:20210427T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/30
DESCRIPTION:Title: Mixing and dissipation properties of transport noise\nby Fr
anco Flandoli (University of Pisa) as part of Necas PDE seminar\n\nLecture
held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstra
ct\nThis talk is based on recent works with Dejun Luo and Lucio\nGaleati d
evoted to the investigation of a suitable scaling limit of\nseveral differ
ent PDE models subject to transport noise\, when the noise\nis extremized
in a suitable limit sense. Among the consequences there\nare certain forms
of mixing\, enhanced dissipation\, delayed blow-up due\nto noise\; these
results hold for several classes of equations including\nEuler and Navier-
Stokes equations\, Keller-Siegel and reaction diffusion\nequations\; and a
lso rigorous results on eddy viscosity and eddy\ndissipation in turbulent
fluids have been proved. Along with arguments\nof stochastic model reducti
on\, developed with Umberto Pappalettera\, a\npicture arises of the potent
ial effects of small scale fluctuations on\nlarge scale properties of turb
ulent fluids.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mythily Ramaswamy (ICTS-TIFR\,India)
DTSTART:20210420T070000Z
DTEND:20210420T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/31
DESCRIPTION:Title: Local stabilization of time periodic flows\nby Mythily Rama
swamy (ICTS-TIFR\,India) as part of Necas PDE seminar\n\nLecture held in B
lue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nFluid
flows have been studied for a long time\, with a view to\nunderstand bett
er the models like channel flow\, blood flow\, air flow in the lungs\netc.
\nHere we focus on time periodic fluid flow models.\nLocal stabilization
here concerns the decay of the perturbation in the\nflow near a periodic t
rajectory.\nThe main motivating example\nis the incompressible Navier-Stok
es system.\nI will discuss the general framework to study periodic solutio
ns\nand then indicate some results in this direction.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nilasis Chaudhuri (TU Berlin)
DTSTART:20210615T070000Z
DTEND:20210615T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/32
DESCRIPTION:Title: Convergence of consistent approximations to the complete compre
ssible Euler system\nby Nilasis Chaudhuri (TU Berlin) as part of Necas
PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitn
a 25\,Prague.\n\nAbstract\nThe aim of the talk is to discuss a result on t
he weak limit of\na `consistent approximation scheme' to the compressible
complete Euler\nsystem in the full space $ \\mathbb{R}^d\,\\\; d=2\,3 $. T
he main result states\nthat if a weak limit of the consistent approximatio
n scheme is a weak\nsolution of the system\, then the approximate solution
s converge locally\nstrongly (or at least almost everywhere) in suitable n
orms under a minimal\nassumption on the initial data of the approximate so
lutions. The class of\nconsistent approximate solutions is quite general a
nd includes the\nvanishing viscosity and heat conductivity limit. In parti
cular\, they do\nnot have to satisfy the minimal principle for entropy.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Oschmann/Peter Bella (University of Dortmund)
DTSTART:20210908T070000Z
DTEND:20210908T100000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/33
DESCRIPTION:Title: Inverse of divergence and homogenization of compressible Navier
-Stokes equations in randomly perforated domains/Regularity for degenerate
elliptic equations\nby Florian Oschmann/Peter Bella (University of Do
rtmund) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Instit
ute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nFlorian Oschmann\n\nInv
erse of divergence and homogenization of compressible Navier-Stokes equati
ons in randomly perforated domains\n\nIn homogenization of compressible Na
vier-Stokes equations\, an inverse of the divergence operator (called Bogi
vski\\u{\\i} operator) is crucial to obtain a-priori bounds for the veloci
ty and density independent of the perforation. Such Bogovski\\u{\\i} opera
tors and bounds are well known in the case of periodically arranged holes
with fixed diameter\, where the mutual distance is of order $\\varepsilon>
0$ and the radii scale like $\\varepsilon^\\alpha$ for some $\\alpha>3$. W
e generalize these results to the case of randomly distributed holes with
random radii and give applications to the homogenization of the Navier-Sto
kes(-Fourier) equations in such randomly perforated domains.\n\nPeter Bell
a\n\nI discuss local regularity properties of solutions of linear\nnon-uni
formly elliptic equations with non-constant coefficients. Assuming certain
integrability conditions on the ellipticity of the coefficient field\, we
obtain local boundedness of weak solutions and corresponding Harnack ineq
uality. The assumed integrability assumptions are sharp and improve upon c
lassical results in the literature (Trudinger). I will also discuss analog
ous result for the time-independent parabolic equations as well as applica
tion to study of the variational integrals with differential (p\,q) growth
.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milan Pokorny (Charles University)
DTSTART:20211005T070000Z
DTEND:20211005T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/34
DESCRIPTION:Title: Steady compressible Navier-Stokes-Fourier system with Dirichlet
boundary conditions for the temperature\nby Milan Pokorny (Charles Un
iversity) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Inst
itute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nBased on recent resul
t by Chaudhuri and Feireisl for the evolutionary NSF system we present the
proof of existence of weak (and variational entropy) solutions to the ste
ady version with Dirichlet boundary conditions for the temperature. The fo
rmulation is based\, similarly as in the evolutionary case\, on a version
of ballistic energy inequality which allows to obtain a priori estimates f
or the temperature and velocity.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil Skrizkovsky (Charles University)
DTSTART:20211019T070000Z
DTEND:20211019T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/35
DESCRIPTION:Title: Evolutionary compressible Navier-Stokes-Fourier system in two s
pace dimensions with adiabatic exponent almost one\nby Emil Skrizkovsk
y (Charles University) as part of Necas PDE seminar\n\nLecture held in Blu
e Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nIn this
talk we consider the full Navier-Stokes-Fourier system and\npresent the pr
oof of the existence of a weak solution in two space\ndimensions for the p
ressure law given by $p(\\varrho\,\\theta) \\sim\n\\varrho\\theta + \\varr
ho \\log^\\alpha(1+\\varrho)+ \\theta^4$\, which can be\nviewed as a close
approximation of the pressure law for ideal gas\n$p(\\varrho\,\\theta) \\
sim \\varrho\\theta$. The weak solutions with entropy\ninequality and tota
l energy balance are considered and the existence of\nthis type of weak so
lutions without any restriction on the size of the\ninitial conditions or
the right-hand sides is shown provided $\\alpha >\n\\frac{17+\\sqrt{417}}{
16}\\cong 2.34$.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danica Basaric (Institute of Mathematics\,CAS)
DTSTART:20211026T070000Z
DTEND:20211026T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/36
DESCRIPTION:Title: Existence of weak solutions for models of general compressible
viscous fluids with linear pressure\nby Danica Basaric (Institute of M
athematics\,CAS) as part of Necas PDE seminar\n\nLecture held in Blue Hall
\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nIn this talk w
e will focus on the existence of weak solutions for a system describing a
general compressible viscous fluid in the case of the pressure being a lin
ear function of the density and the viscous stress tensor being a non-line
ar function of the symmetric velocity gradient. More precisely\, we will f
irst prove the existence of dissipative solutions and study under which co
nditions it is possible to guarantee the existence of weak solutions\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Radosevic (University of Zagreb)
DTSTART:20211102T080000Z
DTEND:20211102T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/37
DESCRIPTION:Title: On the regularity of weak solutions to the fluid-rigid body int
eraction problem\nby Ana Radosevic (University of Zagreb) as part of N
ecas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,
Zitna 25\,Prague.\n\nAbstract\nThe fluid-structure interaction (FSI) syste
ms are multi-physics systems that\ninclude a fluid and solid component. Th
ey are everyday phenomena with a wide\nrange of applications. The simplest
model for the structure is a rigid body. We\nstudy a nonlinear moving bou
ndary fluid-structure interaction problem where the\nfluid flow is governe
d by 3D Navier-Stokes equations\, and the structure is a rigid\nbody descr
ibed by a system of ordinary differential equations called Euler equations
\nfor the rigid body. Our goal is to show that a weak solution that additi
onally\nsatisfy Prodi-Serrin condition is smooth on the interval of its ex
istence\, which is a\ngeneralization of the well-known regularity result f
or the Navier-Stokes equations.\nThis is a joint work with Boris Muha and
Sarka Necasova.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Srdjan Trifunovic (University of Novi Sad)
DTSTART:20211109T080000Z
DTEND:20211109T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/38
DESCRIPTION:Title: On the fluid-structure interaction problem with heat exchange\nby Srdjan Trifunovic (University of Novi Sad) as part of Necas PDE sem
inar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pr
ague.\n\nAbstract\nHere\, I will talk about a nonlinear interaction proble
m between a thermoelastic\nshell and a heat-conducting fluid. The shell is
governed by linear thermoelasticity\nequations and constitutes a time-dep
endent domain which is filled with a fluid\ngoverned by the full Navier-St
okes-Fourier system. The fluid and the shell are fully\ncoupled\, giving r
ise to a new previously unstudied interaction problem involving\nheat exch
ange. The existence of a weak solution for this problem is obtained by\nco
mbining three approximation techniques - decoupling\, penalization and dom
ain\nextension for fluid.\nThis talk is based on a joint work with Václav
Mácha\, Boris Muha\, Šárka\nNečasová and Arnab Roy.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Mitra (University of Wuerzburg)
DTSTART:20211116T080000Z
DTEND:20211116T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/39
DESCRIPTION:Title: A control problem of a linear compressible fluid-structure int
eraction model.\nby Sourav Mitra (University of Wuerzburg) as part of
Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\
,Zitna 25\,Prague.\n\nAbstract\nI will talk about a result on the controll
ability of a compressible FSI model where the structure is located at a p
art of the fluid boundary. I will first introduce the notion of control a
nd explain the tools to prove the controllability of a linear PDE. In the
next part of the talk I will introduce the FSI model under consideratio
n and corresponding linearization. Finally I will speak about the control
of the linearized FSI problem and outline a proof.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patricia Clara (Politechnico di Milano)
DTSTART:20211123T080000Z
DTEND:20211123T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/40
DESCRIPTION:Title: Existence and uniqueness result for a fluid-structure-interacti
on evolution problem in an unbounded 2D channel\nby Patricia Clara (Po
litechnico di Milano) as part of Necas PDE seminar\n\nLecture held in Blue
Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nIn an unb
ounded 2D channel\, we consider the vertical\ndisplacement of a rectangula
r obstacle in a regime of small flux for the\nincoming flow field\, modell
ing the interaction between the cross-section\nof the deck of a suspension
bridge and the wind. We prove an existence\nand uniqueness result for a f
luid-structure-interaction evolution\nproblem set in this channel\, where
at infinity the velocity field of the\nfluid has a Poiseuille flow profile
. We introduce a suitable definition\nof weak solutions and we make use of
a penalty method. In order to\nprevent the obstacle from going excessivel
y far from the equilibrium\nposition and colliding with the boundary of th
e channel\, we introduce a\nstrong force in the differential equation gove
rning the motion of the\nrigid body and we find a unique global-in-time so
lution.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongo Chae (Soeul University)
DTSTART:20211214T080000Z
DTEND:20211214T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/41
DESCRIPTION:Title: canceled\nby Dongo Chae (Soeul University) as part of Necas
PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitn
a 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maja Szlenk (University of Warsaw)
DTSTART:20211130T080000Z
DTEND:20211130T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/42
DESCRIPTION:Title: Uniqueness of weak solutions for the Stokes system for compress
ible fluids with general pressure\nby Maja Szlenk (University of Warsa
w) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute o
f Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe prove existence and uniqu
eness of global in time weak solutions for the Stokes system for compressi
ble fluids with a general\, non-monotone pressure. We construct the soluti
on at the level of Lagrangian formulation and then define the transformati
on to the original Eulerian coordinates. For a nonnegative and bounded ini
tial density\, the solution is nonnegative for all $t>0$ as well and belon
gs to $L^\\infty([0\,\\infty)\\times\\mathbb{T}^d)$. A key point of our co
nsiderations is the uniqueness of such transformation. Since the velocity
might not be Lipschitz continuous\, we develop a method which relies on th
e results of Crippa \\& De Lellis\, concerning regular Lagriangian flows.
The uniqueness is obtained thanks to the application of a certain weighted
flow and detail analysis based on the properties of the $BMO$ space.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong Lu (Nanjing University)
DTSTART:20220104T080000Z
DTEND:20220104T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/43
DESCRIPTION:Title: Global solutions of 2D isentropic compressible Navier-Stokes eq
uations with one slow variable\nby Yong Lu (Nanjing University) as par
t of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathema
tics\,Zitna 25\,Prague.\n\nAbstract\nWe prove the global existence of solu
tions to the two-dimensional isentropic compressible Navier-Stokes equatio
ns with smooth initial data which is slowly varying in one direction and w
ith initial density being away from vacuum. In particular\, we present exa
mples of initial data which generate unique global smooth solutions to 2D
compressible Navier-Stokes equations with constant viscosity and with ini
tial data which are neither small perturbation of constant state nor of sm
all energy.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Baptiste Clément (Czech Technical University)
DTSTART:20220301T080000Z
DTEND:20220301T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/45
DESCRIPTION:Title: Adaptive solution strategy for Richards' equation based on Disc
ontinuous Galerkin methods and mesh refinement\nby Jean-Baptiste Clém
ent (Czech Technical University) as part of Necas PDE seminar\n\nLecture h
eld in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract
\nRichards' equation describes flows in variably saturated\nporous media.
Its solution is challenging since it is a parabolic\nequation with nonline
arities and degeneracies. In particular\, many\nreal-life problems are dem
anding because they can involve\nsteep/heterogeneous hydraulics properties
\, dynamic boundary conditions\nor moving sharp wetting fronts. In this re
gard\, the aim is to design a\nrobust and efficient numerical method to so
lve Richards’ equation.\nTowards this direction\, the work presented her
e deals with\nDiscontinuous Galerkin methods which are very flexible discr
etization\nschemes. They are combined with BDF methods to get high-order\n
solutions. Built upon these desirable features\, an adaptive mesh\nrefinem
ent strategy is proposed to improve Richards’ equation\nsimulations. Exa
mples such as the impoundment of a multi-material dam\nor the groundwater
dynamics of sandy beaches illustrate the abilities\nof the approach.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:holidays
DTSTART:20220308T080000Z
DTEND:20220308T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/46
DESCRIPTION:by holidays as part of Necas PDE seminar\n\nLecture held in Bl
ue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Muha/ Collet GUILLOPÉ (University of Zagreb\, Universite Pa
ris-Est\,Creteil)
DTSTART:20220315T080000Z
DTEND:20220315T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/47
DESCRIPTION:Title: Poroelasticity Interacting with Stokes Flow/About a 1D Green -
Naghdi model with vorticity and surface tension for surface waves\nby
Boris Muha/ Collet GUILLOPÉ (University of Zagreb\, Universite Paris-Est\
,Creteil) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Inst
itute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nBoris Muha\, Universi
ty of Zagreb\nWe consider the interaction between an incompressible\, visc
ous fluid\nmodeled by the dynamic Stokes equation and a multilayered poroe
lastic\nstructure which consists of a thin\, linear\, poroelastic plate la
yer (in direct contact with the free Stokes flow) and a thick Biot layer.
The fluid\nflow and the elastodynamics of the multilayered poroelastic str
ucture are\nfully coupled across a fixed interface through physical coupli
ng conditions\n(including the Beavers-Joseph-Saffman condition)\, which pr
esent mathematical challenges related to the regularity of associated velo
city traces.\nWe prove existence of weak solutions to this fluid-structure
interaction\nproblem with either (i) a linear\, dynamic Biot model\, or (
ii) a nonlinear\nquasi-static Biot component\, where the permeability is a
nonlinear function of the fluid content (as motivated by biological appli
cations). The\nproof is based on constructing approximate solutions throug
h Rothe’s\nmethod\, and using energy methods and a version of Aubin-Lion
s compactness lemma (in the nonlinear case) to recover the weak solution a
s\nthe limit of approximate subsequences. We also provide uniqueness crite
ria and show that constructed weak solutions are indeed strong solutions\n
to the coupled problem if one assumes additional regularity.\nThe presente
d results are joint work with L. Bociu\, S. Canic and J.Webster\n\nGUILLOP
É Colette\nThe Green-Naghdi model is currently the most well-known model\
nused for numerical simulations of waterfront streams\, even\nin setups th
at incorporate vanishing depth (at the shoreline) and wave\nbreaking. Rega
rdless of their many favorable circumstances\, the\nGreen-Naghdi equations
specially take into consideration neglected\nrotational effects\, which a
re significant for wind-driven waves\, waves\nriding upon a sheared curren
t\, waves near a ship\, or tsunami waves\napproaching a shore. The Green-N
aghdi system is first rewritten as an\nequivalent system by using an ad
equate change\nof unknowns. We show that solutions to the model here consi
dered\, with\nvoracity and surface tension\, may be obtained by a standard
Picard\niterative scheme. No loss of regularity is involved with respect\
nto the initial data. Moreover solutions exist at the same level of\nregul
arity as\nfor 1rst order hyperbolic symmetric systems\, i.e. with a regula
rity in\nSobolev spaces of order s > 3/2.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wroblewska
DTSTART:20220322T080000Z
DTEND:20220322T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/48
DESCRIPTION:Title: Two-phase compressible/incompressible Navier-Stokes system with
inflow-outflow boundary conditions\nby Wroblewska as part of Necas PD
E seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 2
5\,Prague.\n\nAbstract\nI will show proof of the existence of a weak solut
ion to the compressible Navier-Stokes system with singular pressure that e
xplodes when density achieves its congestion level. This is a quantity who
se initial value evolves according to the transport equation. We then prov
e that the “stiff pressure" limit gives rise to the two-phase compressib
le/incompressible system with congestion constraint describing the free in
terface. We prescribe the velocity at the boundary and the value of densit
y at the inflow part of the boundary of a general bounded C2 domain. For t
he positive velocity flux\, there are no restrictions on the size of the b
oundary conditions\, while for the zero flux\, a certain smallness is requ
ired for the last limit passage. This result is based on a work with Milan
Pokorný and Ewelina Zatorska.\nReferences:\nM. Pokorný\, A. Wróblewska
-Kamin ́ska\, E. Zatorska. Two-phase compressible/incompressible Navier
–Stokes system with inflow-outflow boundary conditions. arXiv:2202.03557
\, 2022.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ogorzaly
DTSTART:20220405T070000Z
DTEND:20220405T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/49
DESCRIPTION:by Ogorzaly as part of Necas PDE seminar\n\nLecture held in Bl
ue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Angeles Bellido (University of Sevilla)
DTSTART:20220419T070000Z
DTEND:20220419T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/50
DESCRIPTION:Title: Results for a bilinear control problem associated to a repulsiv
e chemotaxis model\nby Maria Angeles Bellido (University of Sevilla) a
s part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Ma
thematics\,Zitna 25\,Prague.\n\nAbstract\nChemotaxis is understood as the
biological process of the movement of living organisms in response to a ch
emical stimulus which can be given towards a higher (attractive) or lower
(repulsive) concentration of a chemical substance. At the same time\, the
presence of living organisms can produce or consume chemical substance.\nI
n this talk\, we study a bilinear optimal control problem associated to a
chemo-repulsion model with linear production term in a 2D and 3D models. T
he existence of a global optimal solution with bilinear control is analyze
d. First-order optimality conditions for local optimal solutions are deriv
ed by using a Lagrange multiplier theorem.\n\nReferences:\n\n[1] Guillén-
González\, F.\; Mallea-Zepeda\, E.\; Rodríguez-Bellido\, M. A.\nOptimal
bilinear control problem related to a chemo-repulsion system in 2D domains
.\nESAIM Control Optim. Calc. Var. 26 (2020)\, Paper No. 29\, 21 pp.\n\n[2
] Guillen-Gonzalez\, F.\; Mallea-Zepeda\, E.\; Rodriguez-Bellido\, M. A.\n
A regularity criterion for a 3D chemo-repulsion system and its application
to a bilinear optimal control problem.\nSIAM J. Control Optim. 58 (2020)\
, no. 3\, 1457–1490.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:He (University of Bielefeld)
DTSTART:20220517T070000Z
DTEND:20220517T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/52
DESCRIPTION:Title: On some two-dimensional incompressible inhomogeneous viscous fl
uid flows\nby He (University of Bielefeld) as part of Necas PDE semina
r\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pragu
e.\n\nAbstract\nIn this talk\, we will present some existence\, uniqueness
and regularity results for the motion of two-dimensional incompressible i
nhomogeneous viscous fluid flows in presence of a density-/temperature-dep
endent viscosity coefficient.\n\nFirstly\, we will discuss the boundary va
lue problem for the stationary Navier-Stokes equation\, where the viscosit
y coefficient is density-dependent. We will give some explicit solutions w
ith piecewise constant viscosity coefficients\, where some regularity and
irregularity results will be considered.\n\nWe will also discuss the initi
al value problem for the evolutionary Boussinesq equation\, which is a non
linear coupling between a heat equation and a Navier-Stokes type of equati
on. In this case\, the viscosity coefficient is temperature-dependent.\n\n
This talk is based on joint work with Xian Liao (KIT).\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gudoshnikov
DTSTART:20220222T080000Z
DTEND:20220222T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/53
DESCRIPTION:Title: Sweeping process and its stability with applications to lattice
s of elasto-plastic springs\nby Gudoshnikov as part of Necas PDE semin
ar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prag
ue.\n\nAbstract\nMoreau's sweeping process is a class of non-smooth evolut
ion problems invented to handle one-sided constraints in natural processes
involving e.g. elastoplasticity\, friction and thresholds in electicity a
nd electomagnetism. The sweeping process can be viewed as a geometric gene
ralization of hysteresis models.\nI will discuss its asymptotic properties
\, especially focusing on the case of a periodic input\, as it leads to pe
riodic outputs forming an attracting set.\nAnother focus will be the stres
s analysis of lattices of elasto-plastic springs via a finite-dimensional
sweeping process (with illustrative examples). The mentioned asymptotic pr
operties lead to nice conclusions about stress trajectories in the lattice
models.\nThis is a joint project with Oleg Makarenkov\, Dmitry Rachinskiy
(University of Texas at Dallas) and Yang Jiao (Arizona State University).
"\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chebbi
DTSTART:20220503T070000Z
DTEND:20220503T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/55
DESCRIPTION:by Chebbi as part of Necas PDE seminar\n\nLecture held in Blue
Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huanyao Wen
DTSTART:20220426T070000Z
DTEND:20220426T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/56
DESCRIPTION:by Huanyao Wen as part of Necas PDE seminar\n\nLecture held in
Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Srdjan Trifunovic (University of Novi Sad)
DTSTART:20220614T070000Z
DTEND:20220614T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/57
DESCRIPTION:Title: Global existence of weak solutions in nonlinear 3D thermoelasti
city\nby Srdjan Trifunovic (University of Novi Sad) as part of Necas P
DE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna
25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Oschmann (Institute of Mathematics\, Czech Academy of Scie
nces)
DTSTART:20221004T070000Z
DTEND:20221004T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/58
DESCRIPTION:Title: An unexpected term for the Oberbeck--Boussinesq approximation\nby Florian Oschmann (Institute of Mathematics\, Czech Academy of Scien
ces) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute
of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nThe Rayleigh-B\\'enard con
vection problem deals with the motion\nof a compressible fluid in a tunnel
heated from below and cooled from\nabove. In this context\, the so-called
Boussinesq relation is used\,\nclaiming that the density deviation from a
constant reference value is a\nlinear function of the temperature. These
density and temperature\ndeviations then satisfy the so-called Oberbeck-Bo
ussinesq equations. The\nrigorous derivation of this system from the full
compressible\nNavier-Stokes-Fourier system was done by Feireisl and Novotn
\\'y for\nconservative boundary conditions on the fluid's velocity and\nte
mperature. In this talk\, we investigate the derivation for Dirichlet\nbou
ndary conditions\, and show that differently to the case of\nconservative
boundary conditions\, the limiting system contains an\nunexpected non-loca
l temperature term. This is joint work with Peter\nBella (TU Dortmund) and
Eduard Feireisl (CAS).\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Simon (Institute of Mathematics)
DTSTART:20221011T070000Z
DTEND:20221011T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/59
DESCRIPTION:Title: CONVERGENCE OF SHAPE DESIGN SOLUTIONS FOR THE NAVIER–STOKES E
QUATIONS\nby John Simon (Institute of Mathematics) as part of Necas PD
E seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 2
5\,Prague.\n\nAbstract\nWe investigate the behavior of dynamic shape desig
n problems for fluid flow at large time horizon.\nIn particular\, we shall
compare the solutions of a dynamic shape optimization problem with that o
f a stationary\nproblem and show that the solution of the former converges
to that of the latter. The convergence of domains\nis based on the $L^\\i
nfty$-topology of their corresponding characteristic functions which is cl
osed under the\nset of domains satisfying the cone property. Lastly\, a nu
merical example is provided to show the occurrence of such convergence.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Höfer (Université de Paris)
DTSTART:20221101T080000Z
DTEND:20221101T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/60
DESCRIPTION:Title: On the derivation of viscoelastic models for Brownian suspensio
ns\nby Richard Höfer (Université de Paris) as part of Necas PDE semi
nar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pra
gue.\n\nAbstract\nWe consider effective properties of suspensions of inert
ialess\, rigid\,\nanisotropic\, Brownian particles in Stokes flows. Recent
years have\nseen tremendous progress regarding the rigorous justification
of\neffective fluid equations for non-Brownian suspensions\, where the\nc
omplex fluid can be described in terms of an effective viscosity. In\ncont
rast to this (quasi-)Newtonian behavior\, anisotropic Brownian\nparticles
cause an additional elastic stress on the fluid. A rigorous\nderivation of
such visco-elastic systems starting from particle models\nis completely m
issing so far. In this talk I will present first\nresults in this directio
n starting from simplified microscopic models\nwhere the particles evolve
only due to rotational Brownian motion and\ncause a Brownian torque on the
fluid. In the limit of infinitely many\nsmall particles with vanishing pa
rticle volume fraction\, we rigorously\nobtain an elastic stress on the fl
uid in terms of the particle density\nthat is given as the solution to an
(in-)stationary Fokker-Planck\nequation.\nJoint work with Marta Leocata (L
UISS Rome) and Amina Mecherbet\n(Université Paris Cité)\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elek Csobo
DTSTART:20221108T080000Z
DTEND:20221108T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/61
DESCRIPTION:by Elek Csobo as part of Necas PDE seminar\n\nLecture held in
Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helmut Abels (University of Regensburg)
DTSTART:20221115T080000Z
DTEND:20221115T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/62
DESCRIPTION:Title: Regularity and Convergence to Equilibrium for a Navier-Stokes-C
ahn-Hilliard System with Unmatched Densities\nby Helmut Abels (Univers
ity of Regensburg) as part of Necas PDE seminar\n\nLecture held in Blue Ha
ll\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe study the
initial-boundary value problem for an incompressible Navier-Stokes-Cahn-H
illiard system with non-constant density proposed by Abels\, Garcke and Gr
ün in 2012. This model arises in the diffuse interface theory for binary
mixtures of viscous incompressible fluids. This system is a generalizatio
n of the well-known model H in the case of fluids with unmatched densities
. In three dimensions\, we prove that any global weak solution (for which
uniqueness is not known) exhibits a propagation of regularity in time and
stabilizes towards an equilibrium state as time tends to infinity. Our ana
lysis hinges upon the following key points: a novel global regularity resu
lt (with explicit bounds) for the Cahn-Hilliard equation with divergence-f
ree velocity belonging only to the Leray-Hopf class\, the energy dissipati
on of the system\, the separation property for large times\, a weak strong
uniqueness type result\, and the Lojasiewicz-Simon inequality.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY://
DTSTART:20221018T070000Z
DTEND:20221018T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/63
DESCRIPTION:by // as part of Necas PDE seminar\n\nLecture held in Blue Hal
l\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY://
DTSTART:20221025T070000Z
DTEND:20221025T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/64
DESCRIPTION:by // as part of Necas PDE seminar\n\nLecture held in Blue Hal
l\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Dębiec (Sorbonne Université)
DTSTART:20221213T080000Z
DTEND:20221213T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/65
DESCRIPTION:Title: On the incompressible limit for some tissue growth models\n
by Tomasz Dębiec (Sorbonne Université) as part of Necas PDE seminar\n\nL
ecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\n
Abstract\nI will discus some approaches to mathematical modelling of\nlivi
ng tissues\, with application to tumour growth. In particular\, I\nwill de
scribe recent results on to the incompressible limit of a\ncompressible mo
del\, which builds a bridge between density-based\ndescription and a geome
tric free-boundary problem by passing to the\nsingular limit in the pressu
re law.\n \n The talk is divided in two parts. First\, I discuss the rate
of\n convergence of solutions of a general class of nonlinear diffusion\n
equations of porous medium type to solutions of a Hele-Shaw-type\n problem
. Then\, I shall present a two-species tissue growth model —\n the main
novelty here is the coupling of both species through the\n so-called Brink
man law which is typically used in the context of\n visco-elastic media\,
where the velocity field is linked to the total\n population pressure via
an elliptic equation.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthieu Cadiot (McGill University)
DTSTART:20230214T080000Z
DTEND:20230214T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/66
DESCRIPTION:Title: Rigorous Computation of Solutions of Semi-Linear Partial Differ
ential Equations on Unbounded Domains Via Spectral Methods\nby Matthie
u Cadiot (McGill University) as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Mitra (Institute of Mathematics\,Czech Academy of Sciences)
DTSTART:20230221T080000Z
DTEND:20230221T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/67
DESCRIPTION:Title: Existence of weak solutions for a compressible multi-component
fluid structure interaction problem\nby Sourav Mitra (Institute of Mat
hematics\,Czech Academy of Sciences) as part of Necas PDE seminar\n\nLectu
re held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbst
ract\nI will speak about our recent work on the analysis of a system of PD
Es governing the interaction between two compressible mutually noninteract
ing fluids and a shell of Koiter type encompassing\na time dependent 3D do
main filled by the fluids. The dynamics of the fluids is modelled by compr
essible Navier-Stokes equations with a physically realistic pressure depen
ding on densities of both the fluids.\nThe shell constitutes the boundary
of the fluid domain and it possesses a non-linear\, non-convex Koiter ener
gy (of a quite general form). We are interested in the existence of a weak
solution to the system until the time-dependent boundary approaches a sel
f-intersection. We first prove a global existence result (until a degenera
cy occurs) when the structure in hyperbolic\, the adiabatic exponents solv
e max{γ\, β} > 2 2 and min{γ\, β} > 0. and further the initial densit
ies are comparable. Next with an extra assumption that the structure is di
ssipative\, we extend our global existence result to the case max{γ\, β}
≥ 2 and min{γ\, β} > 0.\nIn the first part of the talk I will try to
recall a little the classical theory on the existence of weak solutions fo
r compressible mono-fluid models. Next I will talk about our work on the m
ulti-component FSI problem. It is a joint work with M.Kalousek and S.Neca
sova\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Gudoshnikov (Institute of Mathematics\, Czech Academy of Scie
nces)
DTSTART:20230228T080000Z
DTEND:20230228T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/68
DESCRIPTION:by Ivan Gudoshnikov (Institute of Mathematics\, Czech Academy
of Sciences) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, I
nstitute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aneta Wroblewska (Institute of Mathematics\,Polish Academy of Scie
nces)
DTSTART:20230307T080000Z
DTEND:20230307T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/69
DESCRIPTION:Title: Relaxation limit of hydrodynamic models\nby Aneta Wroblewsk
a (Institute of Mathematics\,Polish Academy of Sciences) as part of Necas
PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna
25\,Prague.\n\nAbstract\nWe will show how to obtain general nonlinear agg
regation-diffusion models\,\nincluding Keller-Segel type models with nonli
near diffusions\, as\nrelaxations from nonlocal compressible Euler-type hy
drodynamic systems via\nthe relative entropy method. We plan to discuss th
e assumptions on the\nconfinement and interaction potentials depending on
the relative energy of\nthe free energy functional allowing for this relax
ation limit to hold. We\nwill deal with weak solutions for the nonlocal co
mpressible Euler-type\nsystems and strong solutions for the limiting aggre
gation-diffusion\nequations. Finally\, we will mention how to show the exi
stence of weak\nsolutions to the nonlocal compressible Euler-type systems
satisfying the\nneeded properties for completeness sake. This is a joint r
esult with Jose\nCarrillo and Yingping Peng.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mikhailets (Institute of Mathematics\,Czech Academy of S
ciences)
DTSTART:20230314T080000Z
DTEND:20230314T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/70
DESCRIPTION:Title: One-dimensional differential operators with distributions in co
efficients\nby Volodymyr Mikhailets (Institute of Mathematics\,Czech A
cademy of Sciences) as part of Necas PDE seminar\n\nLecture held in Blue H
all\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nSome classe
s of linear ordinary differential operators with strongly singular coeffic
ients are studied in the talk. These operators are introduced as quasi-dif
ferential according to Shin-Zettl. Their domains may not contain non-zero
smooth functions. The case of self-adjoint Schr\\"{o}dinger and Hill opera
tors on the line is investigated in more detail.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Eiter (Weisstrass Institute\,Berlin)
DTSTART:20230328T070000Z
DTEND:20230328T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/71
DESCRIPTION:Title: The concept of energy-variational solutions for hyperbolic cons
ervation laws\nby Thomas Eiter (Weisstrass Institute\,Berlin) as part
of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathemati
cs\,Zitna 25\,Prague.\n\nAbstract\nWe consider the notion of energy-variat
ional solutions for hyperbolic\nconservation laws. This novel solvability
concept is obtained by\nenriching the variational formulation by the weigh
ted difference\nbetween the mechanical energy and an auxiliary variable re
presenting\nthe turbulent energy. If the weight is chosen suitably\, an ex
istence\nresult for a general class of conservation laws can be derived vi
a a\ntime-discretization scheme based on a sequential minimization and\, i
n\nparticular\, without a spatial regularization. The solution concept\nco
mes along with favorable properties like a weak-strong uniqueness\nprincip
le and the convexity of solution sets. Moreover\, for the\ncompressible an
d incompressible Euler equations\, energy-variational\nsolutions can be id
entified with dissipative weak solutions.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbatiello\, Chaudhuri\, Fasangova
DTSTART:20230404T070000Z
DTEND:20230404T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/72
DESCRIPTION:by Abbatiello\, Chaudhuri\, Fasangova as part of Necas PDE sem
inar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pr
ague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduard Feireisl (Institute of Mathematics\, Czech Academy of Scien
ces)
DTSTART:20230411T070000Z
DTEND:20230411T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/73
DESCRIPTION:Title: Compressible MHD as a dissipative system\nby Eduard Feireis
l (Institute of Mathematics\, Czech Academy of Sciences) as part of Necas
PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna
25\,Prague.\n\nAbstract\nWe show that the compressible MHD system admits
a bounded absorbing\nset in the energy ``norm'' as long as the open bounda
ry\nconditions are imposed. In addition\, the trajectories are precompact\
nin a suitable topology. If this is the case\, there is a compact global\n
attractor as well as statistical stationary solutions supported by\nindivi
dual trajectories of weak solutions.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonin Cesik (Faculty of Mathematics and Physics)
DTSTART:20230321T080000Z
DTEND:20230321T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/74
DESCRIPTION:Title: Inertial evolution of non-linear viscoelastic solids in the fac
e of (self-)collision\nby Antonin Cesik (Faculty of Mathematics and Ph
ysics) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institu
te of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nThe talk discusses exist
ence theory for collisions of (visco-)elastic\nbulk solids which are under
going inertial evolution. In particular\,\nour approach for contact is bas
ed only on the assumption of\nnon-interpenetration of matter. Most other t
heories for contact of\nelastic solids include some phenomenological assum
ptions\, which we do\nnot need in our approach.\n\nWe are able to show exi
stence of weak solutions including contact with\nan obstacle or with the s
olid itself\, for arbitrarily large times and\nlarge deformations. Further
more\, our construction includes a\ncharacterization of the contact force
which obeys conservation of\nmomentum and an energy balance. This contact
force is a vector-valued\nsurface measure acting in the normal direction\,
and is constructed as\na consequence of the non-interpenetration of matte
r.\nThis is a joint work with Giovanni Gravina and Malte Kampschulte.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Oschmann (Institute of Mathematics\,Czech Academy of Scien
ces)
DTSTART:20230502T070000Z
DTEND:20230502T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/75
DESCRIPTION:by Florian Oschmann (Institute of Mathematics\,Czech Academy o
f Sciences) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, In
stitute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University)
DTSTART:20230509T070000Z
DTEND:20230509T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/76
DESCRIPTION:Title: Introduction to free boundary problem for the Navier-Stokes equ
ations and R-solver approach to this problem\nby Yoshihiro Shibata (Wa
seda University) as part of Necas PDE seminar\n\nLecture held in Blue Hall
\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nThis is first
lecture in the series of three lectures by Prof. Shibata.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University)
DTSTART:20230516T063000Z
DTEND:20230516T073000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/77
DESCRIPTION:Title: Maximal L_p-L_q theory for the Stokes equations with free bound
ary conditions\nby Yoshihiro Shibata (Waseda University) as part of Ne
cas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Z
itna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University)
DTSTART:20230523T070000Z
DTEND:20230523T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/78
DESCRIPTION:Title: Local and global well-posedness of free boundary problem for th
e Navier-Stokes equations in exterior domains.\nby Yoshihiro Shibata (
Waseda University) as part of Necas PDE seminar\n\nLecture held in Blue Ha
ll\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Kaplicky (Charles University)
DTSTART:20230418T070000Z
DTEND:20230418T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/79
DESCRIPTION:Title: Stokes problems with dynamic boundary conditions\nby Petr K
aplicky (Charles University) as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe
show maximal regularity in time of solutions to the\nevolutionary Stokes
problem with dynamic boundary condition in the\ncase that the underlying s
pace is Hilbert space.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maja Szlenk (Warsaw University)
DTSTART:20230425T070000Z
DTEND:20230425T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/80
DESCRIPTION:by Maja Szlenk (Warsaw University) as part of Necas PDE semina
r\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pragu
e.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Caggio (Institute of Mathematics\, Czech Academy of Science
s)
DTSTART:20231003T070000Z
DTEND:20231003T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/81
DESCRIPTION:Title: Inviscid limit for the compressible Navier-Stokes equations wit
h density dependent viscosity\nby Matteo Caggio (Institute of Mathemat
ics\, Czech Academy of Sciences) as part of Necas PDE seminar\n\nLecture h
eld in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract
\nWe consider the compressible Navier-Stokes system describing the motion
of a barotropic\nfluid with density dependent viscosity confined in a thre
e-dimensional bounded domain.\nWe show the convergence of the weak solutio
n to the compressible Navier-Stokes system to the strong\nsolution to the
compressible Euler system when the viscosity and the damping coefficients
tend to zero.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yadong Liu (University of Regensburg)
DTSTART:20231114T080000Z
DTEND:20231114T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/82
DESCRIPTION:Title: On a compressible fluid-structure interaction problem with slip
boundary conditions\nby Yadong Liu (University of Regensburg) as part
of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathemat
ics\,Zitna 25\,Prague.\n\nAbstract\nIn this talk\, I will present a projec
t on a compressible barotropic fluid system interacting with a linear (vis
co)-elastic solid equation. In particular\, the elastic structure formulat
es the moving boundary of the fluid\, and the Navier-slip type boundary co
ndition is taken into account. Depending on the reference geometry (flat o
r not)\, I will present the existence of weak solutions to the coupled sys
tem provided the adiabatic exponent satisfies $\\gamma > \\frac{12}{7}$ wi
thout damping and $\\gamma > \\frac{3}{2}$ with structure damping. Moreove
r\, via a modified relative entropy method in time-dependent domains\, I w
ill show you the weak-strong uniqueness property of weak solutions. Finall
y\, I will give a rigorous justification of the incompressible inviscid li
mit of the compressible fluid-structure interaction problem with a flat re
ference geometry\, in the regime of low Mach number\, high Reynolds number
\, and well-prepared initial data. This talk is based on joint work with S
ourav Mitra (IIT\, Indore) and Šárka Nečasová (IMCAS\, Prague).\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyu Liang (LMU Munich\,Germany)
DTSTART:20231121T080000Z
DTEND:20231121T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/83
DESCRIPTION:Title: White noise solutions to mSQG equations\nby Siyu Liang (LMU
Munich\,Germany) as part of Necas PDE seminar\n\nLecture held in Blue Hal
l\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe show exis
tence of white noise solutions for weak\nformulations of modified Surf
ace Quasi-Geostrophic (mSQG) equations.\n Based on previous results on w
hite noise solutions for mSQG\nequations on the torus T^2\, we show a si
milar result for the whole\nspace R^2 by letting the volume of the torus g
o to infinity and\napplying compactness methods (Skorokhod's theorem).\nWe
will present the details on how the kernel on T^2 converges to the\nkerne
l on R^2.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Sokolowski
DTSTART:20231128T080000Z
DTEND:20231128T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/84
DESCRIPTION:by Jan Sokolowski as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neslihan Nesliye Pelen (Ondokuz Mayıs University)
DTSTART:20240109T080000Z
DTEND:20240109T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/85
DESCRIPTION:Title: Vector-Borne Disinformation During Disasters and Emergencies\nby Neslihan Nesliye Pelen (Ondokuz Mayıs University) as part of Necas
PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna
25\,Prague.\n\nAbstract\nDuring disasters and emergencies (earthquakes\,
pandemics\, economic crises\, etc.)\, we also face a second challenge: inf
ormation pollution. The transmitted information may be false\, potentially
harmful\, and speculative. Today\, the main source of information is soci
al media\, which behaves as a vector via sharing news. In this presentatio
n\, the concept of the transmission dynamics of vector-borne diseases is a
dapted to the transmission dynamics of vector-borne disinformation. The dy
namical behavior of the model is analyzed\, the disinformation-free and di
sinformation-endemic equilibria of the model are found\, and both their lo
cal and global stabilities are also discussed. Numerical simulations are a
lso carried out to support the analytical results of the dynamical transmi
ssion of disinformation.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Scherz (University of Würzburg/Charles University)
DTSTART:20240109T091000Z
DTEND:20240109T094000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/86
DESCRIPTION:Title: Weak Solutions to Mathematical Models of the Interaction betwee
n Fluids\, Solids and Electromagnetic Fields\nby Jan Scherz (Universit
y of Würzburg/Charles University) as part of Necas PDE seminar\n\nLecture
held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstra
ct\nWe prove the existence of weak solutions to two systems of PDEs modeli
ng interactions between fluids\, solids and electromagnetic fields. The fi
rst problem we consider describes the motion of an insulating rigid body t
hrough an electrically conducting incompressible fluid. The existence of w
eak solutions to this problem is achieved via a time discretization and an
application of the Brinkman penalization. The second considered problem d
eals with the evolution of the deformation and the magnetization of a magn
etoelastic material and is solved via an application of De Giorgi's minimi
zing movements scheme.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Gavioli
DTSTART:20240220T080000Z
DTEND:20240220T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/87
DESCRIPTION:by Chiara Gavioli as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisabeta Rocca (University of Pavia)
DTSTART:20240521T063000Z
DTEND:20240521T073000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/88
DESCRIPTION:Title: From non local to local Cahn-Hilliard-Reaction-Diffusion model
for tumor growth\nby Elisabeta Rocca (University of Pavia) as part of
Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\
,Zitna 25\,Prague.\n\nAbstract\nIn this seminar we discuss about a recent
joint work with Elisa Davoli\,\nLuca Scarpa and Lara Trussardi where we st
udy a nonlocal-to-local\nasymptotics for a tumor-growth model coupling a v
iscous Cahn-Hilliard\nequation describing the tumor proportion with a reac
tion-diffusion\nequation for the nutrient phase parameter. First\, we prov
e that\nsolutions to the nonlocal Cahn-Hilliard system converge\, as the\n
nonlocality parameter tends to zero\, to solutions to its local\ncounterpa
rt. Second\, we provide first-order optimality conditions for an\noptimal
control problem on the local model\, accounting also for\nchemotaxis\, and
both for regular or singular potentials\, without any\nadditional regular
ity assumptions on the solution operator.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Simon (Austrian Academy of Sciences)
DTSTART:20240305T080000Z
DTEND:20240305T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/89
DESCRIPTION:Title: Analysis of Unregularized Optimal Control Problems Constrained
by the Boussinesq System\nby John Simon (Austrian Academy of Sciences)
as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of
Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe investigate solution stabil
ity of unregularized tracking-type optimal control problems constrained by
the Boussinesq system. In our model\, the controls may appear linearly an
d distributed in both of the equations that constitute the Boussiniesq sys
tem and in the objective functional. We establish\, not only the existence
of weak solutions\, but also unique existence of strong solutions in $L^p
$ sense for the Boussinesq system as well as its corresponding linearized
and adjoint systems. The optimal control problem is then analyzed by provi
ding the existence of an optimal control\, and by establishing first-order
necessary and second order sufficient conditions. Then\, using assumption
s on the joint growth of the first and second variations of the objective
functional\, we prove the strong metric Hölder subregularity of the optim
ality mapping\, which in turn allows the study of solution stability of th
e optimal control and states under various linear and nonlinear perturbati
ons. Such perturbations may appear in the Boussinesq system and the object
ive functional. As an application\, we provide a convergence rate for the
optimal solutions of the Tikhonov regularized problem as the Tikhonov para
meter tends to zero. Furthermore\, the obtained stability of the optimal s
tates provides stability of the second-order sufficient condition in affin
e PDE-constrained optimization under an assumption on the desired profile
which is natural for tracking-type objective functionals.\n\n\n\nThis is a
joint work with Nicolai Jork.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Lancmanova (Czech Technical University)
DTSTART:20240312T080000Z
DTEND:20240312T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/90
DESCRIPTION:Title: Numerical Study of the Steady Airflow in the Human Respiratory
System During Inhaling and Exhaling\nby Anna Lancmanova (Czech Technic
al University) as part of Necas PDE seminar\n\nLecture held in Blue Hall\,
Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nThis paper prese
nts some of the initial results of the numerical simulations of a steady t
urbulent flow in human upper airways during inhalation and exhalation. The
mathematical model is based on the system of Reynolds-Averaged incompress
ible Navier-Stokes equations complemented by the SST k − ω turbulence m
odel. The simulations were performed using the finite-volume open-source s
olver OpenFOAM on a realistic three-dimensional geometry. The main aim of
this particular study is to verify the computational setup with a special
focus on the appropriate choice and implementation of boundary conditions.
The prescribed boundary conditions are chosen to mimic the physiological
conditions during a normal breathing cycle. This study aims to gain insigh
t into the airflow behavior during the inhalation and exhalation process b
y comparing the results of two distinct simulations corresponding to two d
ifferent (opposite) flow rates. The obtained local flow rates and flow fie
lds for both cases are presented and mutually compared. This initial work
should serve as a foundation for future more complex simulations that will
include the time-dependent and compressible effects.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomas Roubicek
DTSTART:20240326T080000Z
DTEND:20240326T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/91
DESCRIPTION:Title: Thermomechanical models for finitely-strained viscoelastic soli
ds and related mathematical aspects\nby Tomas Roubicek as part of Neca
s PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zit
na 25\,Prague.\n\nAbstract\nModels of visco-elastodynamic solids at finite
strains will be presented and the Lagrangian versus Eulerian formulation
will be discussed. Mathematical analysis using some gradient theories will
be outlined and some impacts of these higher gradients on dispersion and
attenuation of wave propagation will be discussed\, too. Also coupled ther
momechanical problems will be presented\, allowing for heat capacity degen
erating to zero at zero temperature\, which is also a physically relevant
attribute related with non-negativity of entropy.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiri Neustupa (Institute of Mathematics\,Czech Academy of Sciences
)
DTSTART:20240402T070000Z
DTEND:20240402T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/92
DESCRIPTION:Title: On steady solutions to the MHD equations with inhomogeneous gen
eralized impermeability boundary conditions for the magnetic field\nby
Jiri Neustupa (Institute of Mathematics\,Czech Academy of Sciences) as pa
rt of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathem
atics\,Zitna 25\,Prague.\n\nAbstract\nWe deal with the steady MHD equation
s for a viscous incompressible fluid with the no--slip boundary condition
for the velocity $u$ and the inhomogeneous version of the so called genera
lized impermeability boundary conditions for the magnetic field $b$. We ex
plain the sense of these conditions. The main results concern an appropria
te definition of the weak solution $(u\,b)$\, its existence\, continuous d
ependence on the data when the data tend to zero and uniqueness in a ``sma
ll'' neighborhood of the zero solution $u=0$\, $b=0$.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rinaldo Colombo (University of Brescia)
DTSTART:20240409T070000Z
DTEND:20240409T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/93
DESCRIPTION:Title: Hyperbolic Techniques in Biological Models\nby Rinaldo Colo
mbo (University of Brescia) as part of Necas PDE seminar\n\nLecture held i
n Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nCon
servation (or Balance) Laws enter a variety of biological\nmodels. In popu
lation dynamics\, balance laws describe age (or space)\nstructured dynamic
s. In epidemiology\, balance laws enter several\nvariazioni on the SIR mod
el. In predator prey dynamics\, non local\nbalance laws describe species m
oving with finite speed towards a well\ndefined target. Other examples of
the use of these equations are\nprovided by cancer or cell growth.\n\nThis
talk presents some analytical results related to the the above\nmodels\,
hoping to foster the discussion also on the modeling and on\nthe numerical
issues involved.\n\nJoint work with M. Garavello (University of Milano -
Bicocca)\,\nF. Marcellini (University of Brescia) and E. Rossi (University
of\nModena - Reggio Emilia).\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Hajduk
DTSTART:20240416T070000Z
DTEND:20240416T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/94
DESCRIPTION:by Karol Hajduk as part of Necas PDE seminar\n\nLecture held i
n Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Caggio (Institute of Mathematics\, Czech Academy of Science
s)
DTSTART:20240507T070000Z
DTEND:20240507T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/96
DESCRIPTION:Title: Vanishing viscosity limit for the compressible Navier-Stokes eq
uations with non-linear density dependent viscosities\nby Matteo Caggi
o (Institute of Mathematics\, Czech Academy of Sciences) as part of Necas
PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna
25\,Prague.\n\nAbstract\nIn a three-dimensional bounded domain\, we consi
der the compressible\nNavier-Stokes equations\nfor a barotropic fluid with
general non-linear density dependent\nviscosities and no-slip boundary\nc
onditions. A nonlinear drag term is added to the momentum equation.\nWe es
tablish two\nconditional Kato-type criteria for the convergence of the wea
k\nsolutions to such a system\ntowards the strong solution of the compress
ible Euler system when the\nviscosity coefficient\nand the drag term param
eter tend to zero.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Imene DJEBOUR (CY Cergy–Paris Université)
DTSTART:20240604T070000Z
DTEND:20240604T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/97
DESCRIPTION:Title: Existence of strong solutions for a compressible fluid-solid in
teraction system with Navier slip boundary conditions\nby Imene DJEBOU
R (CY Cergy–Paris Université) as part of Necas PDE seminar\n\nLecture h
eld in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract
\nWe consider a fluid-structure interaction system coupling a viscous\nflu
id governed by the compressible Navier-Stokes equations and a rigid\nbody
immersed in the fluid and modeled by the Newton's law. In this\nwork\, we
consider the Navier slip boundary conditions. Our aim is to\nshow the loca
l in time existence and uniqueness of the strong solution\nto the correspo
nding problem. The main step of this work is that we use\nLagrangian chang
e of variables in order to handle the transport equation\nand to reduce th
e problem in the initial domain. The strategy is based\non the study of th
e linearized system with nonhomogeneous boundary\nconditions and on the Ba
nach fixed point theorem.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akash Parmar (University of Warsaw)
DTSTART:20240507T082000Z
DTEND:20240507T092000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/98
DESCRIPTION:Title: Optimal regularity for conservation laws with discontinuous flu
x and large data existence for the isentropic Euler equations\nby A
kash Parmar (University of Warsaw) as part of Necas PDE seminar\n\nLecture
held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstra
ct\nIn this talk\, first\, we discuss the regularity aspects of the scalar
\nconservation laws with discontinuous flux. The optimal regularity of the
\nentropy solution has been an open question since 2011 [Adimurthi et. al\
,\nComm. Pure Appl. Math.\, 2011]\, as they established that the entropy\n
solution of scalar conservation laws with discontinuous flux does not\nbel
ong to BV space even when the initial data is in BV. We prove the\noptimal
regularity of the entropy solution for bounded initial data in\nthe "frac
tional BV" space\, (i.e.\, we prove the Lax-Oleinik type\nregularizing e
ffect). Furthermore\, we demonstrate the higher regularity\nof the entropy
solution in the "fractional BV" space for the\ngeometrically restricted
fluxes. In the second part of the talk\, we\ndiscuss the global existence
of a weak solution for the isentropic Euler\nequation in one space dimensi
on with large initial data in BV. We use\nGlimm's scheme to get the approx
imate weak solution and then Riemann\ninvariant to get the uniform bounds
of the total variation. We also\nprovide a criterion under which the total
variation of Riemann\ninvariants decays.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Kaplicky
DTSTART:20240430T070000Z
DTEND:20240430T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/99
DESCRIPTION:by Petr Kaplicky as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong Lyu (Nanjing University)
DTSTART:20240521T080000Z
DTEND:20240521T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/100
DESCRIPTION:Title: Unconditional stability of equilibria in thermally driven comp
ressible fluids\nby Yong Lyu (Nanjing University) as part of Necas PDE
seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25
\,Prague.\n\nAbstract\nWe show that small perturbations of the spatially h
omogeneous equilibrium of a thermally driven compressible viscous fluid ar
e globally stable. Specifically\, any weak solution of the evolutionary Na
vier-Stokes-Fourier system driven by thermal convection converges to an eq
uilibrium as time goes to infinity. The main difficulty to overcome is the
fact the problem does not admit any obvious Lyapunov function. The result
applies\, in particular\, to the Rayleigh-Bénard convection problem.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kuntal Bhandari (Institute of Mathematics\, CAS)
DTSTART:20241015T070000Z
DTEND:20241015T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/101
DESCRIPTION:Title: On the controllability of some chemotaxis model via Carleman a
pproach\nby Kuntal Bhandari (Institute of Mathematics\, CAS) as part o
f Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematic
s\,Zitna 25\,Prague.\n\nAbstract\nWe present the controllability property
for a chemotaxis-type system. The model is a $3\\times 3$ nonlinear parabo
lic-elliptic system with nonlocal couplings. The null-controllability of t
he associated linearized system is established through the well-known Carl
eman techniques and then we apply some fixed point strategy to prove the l
ocal null-controllability of the actual system. The main difficulty is to
manage the nonlocal terms while proving a suitable Carleman estimate for t
he adjoint to the concerned system.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reinhard Farwig (TH Darmstadt)
DTSTART:20241029T080000Z
DTEND:20241029T093000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/102
DESCRIPTION:Title: An Approach to the Navier-Stokes System on Exterior Domains in
Weighted Function Spaces I\nby Reinhard Farwig (TH Darmstadt) as par
t of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathema
tics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reinhard Farwig (TH Darmstadt)
DTSTART:20241105T080000Z
DTEND:20241105T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/103
DESCRIPTION:Title: An Approach to the Navier-Stokes System on Exterior Domains in
Weighted Function Spaces II\nby Reinhard Farwig (TH Darmstadt) as pa
rt of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathem
atics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mostafa Meliani (Institute of Mathematics\, CAS)
DTSTART:20241105T092000Z
DTEND:20241105T102000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/104
DESCRIPTION:by Mostafa Meliani (Institute of Mathematics\, CAS) as part of
Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics
\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Piasecki (University of Warsaw)
DTSTART:20241203T080000Z
DTEND:20241203T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/105
DESCRIPTION:Title: Stability of the density patches problem with vacuum for incom
pressible inhomogeneous viscous flows\nby Tomasz Piasecki (University
of Warsaw) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Ins
titute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nThe talk is based on
a joint work with Piotr B. Mucha and Raphael Danchin.\nWe consider the in
homogeneous incompressible\nNavier-Stokes system in a smooth two or three
dimensional bounded domain\,\nin the case where the initial density is onl
y bounded.\nExistence and uniqueness for such initial data was shown recen
tly by R.\nDanchin and P.B. Mucha\, but the stability issue was left open.
\nThe point is that the difference of initial densities may be non-zero on
a\nset where one of the densities vanishes\,\ntherefore the proof on uniq
ueness does not imply stability\, like in case\nwithout vacuum. In the tal
k I will focus on the issue of stability.\nAfter observing that the soluti
ons have exponential decay\, which is a result of\nindependent interest\,
we prove stability with respect to initial data\,\nfirst in Lagrangian coo
rdinates\, and then in the Eulerian frame.\n\nIn particular\, our stabilit
y estimates are not weighted by the initial\ndensities. Hence\, our result
applies in particular to the classical\ndensity patches problem\, where t
he density is a characteristic function.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Lewandowski (University of Rennes)
DTSTART:20241217T080000Z
DTEND:20241217T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/106
DESCRIPTION:Title: Degenerate elliptic equations with a source term in $L^1$\nby Roger Lewandowski (University of Rennes) as part of Necas PDE semina
r\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pragu
e.\n\nAbstract\nLet $\\Omega$ be a domain in $\\R^N$\, where $N=2\, 3$\, a
nd $\\Gamma$ its boundary. We consider an elliptic equation with coefficie
nts that degenerate as $d(x\, \\Gamma)^\\beta$\, where $d(x\, \\Gamma)$ de
notes the distance to the boundary\, $0 < \\beta <1$\, and a source term i
n $L^1$\, a problem arising in turbulence modeling. We will detail how to
obtain sharp estimates in Sobolev spaces using the so-called "washer metho
d\," and then prove the existence of a distributional solution when $0 < \
\beta < \\beta_c < 1$\, for a critical exponent $\\beta_c$. We will then c
onsider more general problems with a similar structure.\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aneta Wróblewska-Kamińska (Institute of Mathematics of the Polis
h Academy of Sciences\, Poland)
DTSTART:20260317T080000Z
DTEND:20260317T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/107
DESCRIPTION:Title: Coupled Vlasov and non-Newtonian dynamics\nby Aneta Wróbl
ewska-Kamińska (Institute of Mathematics of the Polish Academy of Science
s\, Poland) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, In
stitute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuấn Tùng Nguyễn (Technische Universität Wien)
DTSTART:20260317T092000Z
DTEND:20260317T102000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/108
DESCRIPTION:Title: Time-Uniform Bounds for Instationary Three - Species Drift-Dif
fusion Equations for Memristors\nby Tuấn Tùng Nguyễn (Technische
Universität Wien) as part of Necas PDE seminar\n\nLecture held in Blue Ha
ll\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kružík (Institute of Information Theory and Automation)
DTSTART:20260324T080000Z
DTEND:20260324T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/109
DESCRIPTION:Title: Hadamard’s inequality in the mean\nby Martin Kružík (I
nstitute of Information Theory and Automation) as part of Necas PDE semina
r\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pragu
e.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Oschmann (Charles University)
DTSTART:20260331T070000Z
DTEND:20260331T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/110
DESCRIPTION:Title: Per aquam ad astra: on stars (and) boiling water\nby Flori
an Oschmann (Charles University) as part of Necas PDE seminar\n\nLecture h
eld in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malte-Laurens Kampschulte (Charles University)
DTSTART:20260414T070000Z
DTEND:20260414T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/111
DESCRIPTION:by Malte-Laurens Kampschulte (Charles University) as part of
Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\
,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josef Janak
DTSTART:20260408T070000Z
DTEND:20260408T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/112
DESCRIPTION:by Josef Janak as part of Necas PDE seminar\n\nLecture held in
Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Borja Rukavina (University of Zagreb)
DTSTART:20260512T070000Z
DTEND:20260512T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/113
DESCRIPTION:by Borja Rukavina (University of Zagreb) as part of Necas PDE
seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\
,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iulia Cristian (Sorbonne Université)
DTSTART:20260519T070000Z
DTEND:20260519T080000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/114
DESCRIPTION:by Iulia Cristian (Sorbonne Université) as part of Necas PDE
seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\
,Prague.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Sauer (University of Jena)
DTSTART:20260326T080000Z
DTEND:20260326T090000Z
DTSTAMP:20260404T094504Z
UID:TuesdayPDE/115
DESCRIPTION:Title: Mixed-Order System with General Boundary Conditions\nby Jo
nas Sauer (University of Jena) as part of Necas PDE seminar\n\nLecture hel
d in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/TuesdayPDE/115/
END:VEVENT
END:VCALENDAR