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BEGIN:VEVENT
SUMMARY:G.Paolo Galdi (University of Pittsburgh\, USA)
DTSTART:20201112T130000Z
DTEND:20201112T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/1
DESCRIPTION:Title: On the Self-Propelled Motion of a Rigid Body in a V
iscous Liquid by Time-Periodic Boundary Data\nby G.Paolo Galdi (Univer
sity of Pittsburgh\, USA) as part of Fudan International Seminar on Analys
is\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe consider a body\, $\\mat
hcal B$\, moving in a Navier-Stokes liquid and subject to a driving\nmecha
nism constituted by a time-periodic distribution of velocity\, $\\mathbf v
_*$\, at the interface\nbody-liquid. This study is mostly motivated by und
erstanding the vibration-induced\npropulsion of objects of fixed shape mov
ing in a viscous liquid. More precisely\, we aim\nat characterizing the th
rust and its relation to the translational velocity of $\\mathcal B$. With
\nthis in mind\, we show that\, in a suitable class of weak solutions\, if
the average over a\nperiod of $\\mathbf v_*$\, $\\bar\\mathbf v_*$ is not
zero\, then $\\mathcal B$ will propel itself on the condition that $\\bar
\\mathbf v_*$ has a non-vanishing projection on a suitable “control” s
pace. This result is achieved by using a suitable perturbation argument ar
ound a linearized solution. If\, however\, $\\bar\\mathbf v_*=0$ (purely o
scillatory case\, like in the vibration-induced motion)\, we then show tha
t self-propulsion is a strictly nonlinear phenomenon and that it occurs if
and only if $\\bar\\mathbf v_*$ satisfies a suitable non-local condition.
\n\nThe recorded talk is available\, see the above link\, Passcode: X!Pi=
V2A\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Panasenko (Institute Camille Jordan UMR CNRS 5208\, Univer
sity Jean Monnet\, Saint-Etienne\, France)
DTSTART:20201203T130000Z
DTEND:20201203T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/2
DESCRIPTION:Title: Asymptotic coupling of models of different dimensio
ns: MAPDD\nby Grigory Panasenko (Institute Camille Jordan UMR CNRS 520
8\, University Jean Monnet\, Saint-Etienne\, France) as part of Fudan Inte
rnational Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\n
The lecture is devoted to the problem of coupling of models of different d
imension. Many real world problems are related to solving partial differen
tial equations in domains of complex geometry\, combining multiple thin pa
rts with massive parts: the set of blood vessels\, structures in aircraft
and spacecraft\, industrial installations\, pipelines with reservoirs. The
direct numerical computations with standard codes are impossible because
such complex geometry needs a very fine mesh “feeling” all elements of
the structure and so the 3D computations need too much time-memory resour
ces. That is why the dimension reduction is a very popular trend in reduci
ng computational cost\, however the completely reduced model loses very im
portant local information and are not precise. For example\, in the blood
circulation modelling [1] one-dimensional models are widely applied\, but
the description of the clot formation\, blood flow near a stent need 3D lo
cal zoom. How to glue the models of different dimension? The lecture prese
nts an asymptotic approach to this problem\, based on asymptotic analysis
of partial differential equations in domains containing thin parts\, conne
cted sets of thin cylinders. For example the Navier-Stokes equations are u
sed in hemodynamic modeling. We present the method of partial asymptotic d
ecomposition of domains (MAPDD) [2-6] giving a high precision coupling of
models of different dimension.\n \nFormaggia\,L.\, Quarteroni\,A.\, Vene
ziani A.\, Cardiovascular Mathematics: Modeling and simulation of the circ
ulatory system\, Springer Science and Business Media\, 2010.\n2.
Panasenko G.\, Method of asymptotic partial decomposition of
domain\, Mathematical Models and Methods in Applied Sciences \, 8\,1\, 199
8\, 139-156.\nPanasenko G.\, Multi-Scale Modelling for Structures and Comp
osites\, Springer\, Dordrecht\, 2005. \nPanasenko G.\, Method of asymptot
ic partial decomposition of domain for multistructures\, Applicable Analys
is\, 2017\, 96\, 16\, 2771-2779\, http://dx.doi.org/10.1080/00036811.2016.
1240366\nPanasenko G.\, Pileckas K.\, Asymptotic analysis of the non-stead
y Navier-Stokes equations in a tube structure.I. The case without boundary
layer-in-time. Nonlinear Analysis\, Series A\, Theory\, Methods and Appli
cations\, 122\, 2015\, 125-168\, http://dx.doi.org/10.1016/j.na.2015.03.00
8\nBertoglio C.\, Conca C.\, Nolte D.\, Panasenko G.\, Pileckas K.\, Junct
ion of models of different dimension for flows in tube structures by Womer
sley-type interface conditions\, SIAM J. Appl.Math. 2019 79\, 3\, 959-985
doi.10.1137/M1229572\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Volberg (Michigan State University)
DTSTART:20201119T130000Z
DTEND:20201119T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/3
DESCRIPTION:Title: Removable singularities for Lipschitz harmonic func
tions\, Geometric Measure Theory\, and fine structure of harmonic measure<
/a>\nby Alexander Volberg (Michigan State University) as part of Fudan Int
ernational Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\
nWhat are the removable singularities of harmonic functions with bounded g
radient? This problem\, that takes its origins in certain problems of com
plex analysis\, which are 140 years old was solved recently. It is a free
boundary problem and its solution (which we will explain) is based on exte
nsion to a new territory of classical theory of singular integrals.\nSingu
lar integrals are ubiquitous objects. The simplest ones are called Caldero
n–Zygmund operators. Their theory was completed in the 50′s by Zygmund
and Calderon. Or it seemed like that. The last 20 years saw the need to c
onsider CZ operators in\nvery bad environment\, so kernels are still very
good\, but the ambient set/measure has no regularity whatsoever.\nInitiall
y\, such situations appeared from the wish to solve some outstanding probl
ems in complex analysis: such as problems of Painlev\\’e\, Ahlfors’\,
Denjoy’s\, and Vitushkin’s.\nThe analysis of CZ operators on very bad
sets is also very fruitful in the part of Geometric Measure Theory that de
als with removability mentioned above and rectifiability. It can be viewed
as the study of very low regularity free boundary problems. We will expl
ain the genesis of ideas that led to several long and difficult proves tha
t culminated in our solution to problems of Denjoy\, Vitushkin and Guy Dav
id\, and also brought the solution by Tolsa of Painlev\\’e’s problem.\
n\nThe passcode to the recorded video is\n^98qdTub\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao Ren (任潇) (Fudan University)
DTSTART:20201126T130000Z
DTEND:20201126T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/4
DESCRIPTION:Title: The uniqueness of Plane Stationary Navier-Stokes Fl
ow Past an Obstacle\nby Xiao Ren (任潇) (Fudan University) as part o
f Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n
\nAbstract\nWe study the exterior problem for stationary Navier-Stokes equ
ations in two dimensions describing a viscous incompressible fluid flowing
past an obstacle. It is shown that\, at small Reynolds numbers\, the clas
sical solutions constructed by Finn and Smith are unique in the class of D
-solutions (i.e.\, solutions with finite Dirichlet integral). No additiona
l symmetry or decay assumptions are required. This result answers a long-s
tanding open problem. The talk is based on a joint paper with M.Korobkov.\
n\nThe passcode for the recorded video\n=$!02mLv\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shnirelman (Concordia University\, Montreal\, Quebec\, C
anada)
DTSTART:20201210T130000Z
DTEND:20201210T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/5
DESCRIPTION:Title: Turbulent weak solutions of the Euler equations
\nby Alexander Shnirelman (Concordia University\, Montreal\, Quebec\, Cana
da) as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid
mechanics\n\n\nAbstract\nTurbulence is the property of flows of an incompr
essible fluid at very high Reynolds number\, or\, equivalently\, at very s
mall viscosity. The most prominent feature of turbulent flows is a conside
rable rate of the energy dissipation which is nearly independent on the vi
scosity provided the latter is small enough. It is natural to consider the
case of infinitesimally small viscosity in the hope that there exists a m
eaningful limit of viscous flows as the viscosity tends to zero. In the li
mit the flows are described by some sort of weak solutions of the Euler eq
uations. However\, there exist a lot of examples of weak solutions (Scheff
er\, Shnirelman\, De Lellis\, Szekekyhidi\, Buckmaster\, Vicol\, and other
s) whose behavior is far from what is expected from the models of turbulen
t flows. Those weak solutions are definitely non-physical.\n \n\nIn this t
alk I'm going to describe a new class of weak solutions of the Euler equat
ions which might have more physical content. Their construction is based o
n the combination of several ideas: (a) Comprehensive Lagrangian descripti
on of irregular flows is equivalent to some class of random processes. (b)
Fluid flows correspond to the motion along a very non-regular set in a Hi
lbert space. (c) The motion on such set can be described by the generalize
d D'Alembert Principle which implies the energy dissipation even in the ab
sence of friction (or viscosity). This statement is illustrated by simple
model examples. (d) The accurate formulation of the above principle requir
es the use of the Nonstandard Analysis (NSA). (e) The above components imp
ly the existence of a weak solution for any initial velocity of finite ene
rgy.\nHowever\, the study of the properties of those solutions requires fu
rther work.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Sperone (Department of Mathematical Analysis\, Faculty o
f Mathematics and Physics\, Charles University in Prague)
DTSTART:20201217T130000Z
DTEND:20201217T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/6
DESCRIPTION:Title: Explicit bounds for the generation of a lift force
exerted by steady-state Navier-Stokes flows over a fixed obstacle\nby
Gianmarco Sperone (Department of Mathematical Analysis\, Faculty of Mathem
atics and Physics\, Charles University in Prague) as part of Fudan Interna
tional Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe
analyze the steady motion of a viscous incompressible fluid\nin a two- and
three-dimensional channel containing an obstacle through\nthe Navier-Stok
es equations under different types of boundary\nconditions. In the 2D case
we take constant non-homogeneous Dirichlet\nboundary data in a (virtual)
square containing the obstacle\, and\nemphasize the connection between the
appearance of lift and the unique\nsolvability of Navier-Stokes equations
. In the 3D case we consider mixed\nboundary conditions: the inflow is giv
en by a fairly general datum and\nthe flow is assumed to satisfy a constan
t traction boundary condition on\nthe outlet. In the absence of external f
orcing\, explicit bounds on the\ninflow velocity guaranteeing existence an
d uniqueness of such steady\nmotion are provided after estimating some Sob
olev embedding constants\nand constructing a suitable solenoidal extension
of the inlet velocity.\nIn the 3D case\, this solenoidal extension is bui
lt through the Bogovskii\noperator and explicit bounds on its Dirichlet no
rm (in terms of the\ngeometric parameters of the obstacle) are found by so
lving a variational\nproblem involving the infinity-Laplacian.\nThe talk a
ccounts for results obtained in collaboration with Filippo\nGazzola and Il
aria Fragalà (both at Politecnico di Milano).\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University\, Tokyo\, Japan)
DTSTART:20210114T130000Z
DTEND:20210114T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/7
DESCRIPTION:Title: R-bounded solution operators and mathematical fluid
dynamics\nby Yoshihiro Shibata (Waseda University\, Tokyo\, Japan) as
part of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechan
ics\n\n\nAbstract\nI would like to explain a systematic method of obtainin
g the maximal regularity\nof solutions for a system of a linear parabolic
equations with non-homogeneous \nboundary conditions based on R-solution o
perators for the resolvent problem\nwith non-homogeneous boundary conditio
ns. In fact\, combination of \nR-bounded solution operators with the Wei
s operator\nvalued Fourier multiplier theorem and extension of de Leeuv tr
ansference theorem\nto the operator valued Fourier multiplier yield the ma
ximal regularity theorem\nfor the initial boundary value problem for linea
r parabolic systems with non-homogeneous\nboundary conditions and high fre
quency part of periodic solutions for linear\nparabolic system with non-ho
mogeneous boundary conditions. \n\nAs application of our approach based on
R-bounded solution operators\,\nI discuss the local and global well pose
dness of a free boundary problem for the Navier-Stokes equations in an ext
erior domain\, and the unique existence theorem of periodic solutions of\n
the Navier-Stokes equations in a periodically moving three dimensional dom
ain.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Reinhard Farwig (TU Darmstadt\, Germany)
DTSTART:20210121T130000Z
DTEND:20210121T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/8
DESCRIPTION:Title: The Navier-Stokes Equations in Bounded Domains with
Moving Boundaries\nby Professor Reinhard Farwig (TU Darmstadt\, Germa
ny) as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid
mechanics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Paolo Maremonti (Università della Campania Luigi Vanvit
elli\, Caserta\, Italy)
DTSTART:20210218T130000Z
DTEND:20210218T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/9
DESCRIPTION:Title: On the uniqueness of a suitable weak solution to th
e Navier-Stokes Cauchy problem\nby Professor Paolo Maremonti (Universi
tà della Campania Luigi Vanvitelli\, Caserta\, Italy) as part of Fudan In
ternational Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract
\nWe are dealing with the Navier-Stokes Cauchy problem. We investigate som
e results of regularity and uniqueness related to suitable weak solutions.
The suitable weak solution notion is meant in the sense introduced by Caf
farelli-Kohn-Nirenberg. In paper [1]\, we recognize that a suitable weak s
olution enjoys more regularity than Leray-Hopf weak solutions\, that allow
s us to furnish new uniqueness results for the solutions. Actually\, we re
alize two results. The first one is a new sufficient condition on the init
ial datum u0 for uniqueness. We work on existing suitable weak solution\,
that is\, we do not construct a more regular weak solution corresponding t
o our initial datum. The second result employs a weaker condition with res
pect to previous ones (almost u0 is in L2)\, but\, just for one of the two
compared weak solutions\, we need a “special" Prodi-Serrin condition. I
t is “special" as it is local in space.\n\nReferences\n\n[1] Crispo F. a
nd Maremonti P.\, On the uniqueness of a suitable weak solution to the Nav
ier-Stokes Cauchy problem\, SN Partial Di_erential Equations and Applicati
ons\, to appear.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Kristensen (University of Oxford)
DTSTART:20210225T130000Z
DTEND:20210225T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/10
DESCRIPTION:Title: Garding inequalities and their impact on regularit
y and uniqueness\nby Jan Kristensen (University of Oxford) as part of
Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\n
Abstract\nMinimizers of strongly quasiconvex variational integrals need no
t be regular nor unique.\nHowever\, if a suitable G{\\aa}rding type inequa
lity is assumed for the variational integral\, then both regularity and un
iqueness of minimizers can be restored under natural smallness conditions
on the data. In turn\, the G{\\aa}rding inequality turns out to always hol
d under an a priori C1 regularity hypothesis on the minimizer\, while its
validity is not known in the\ngeneral case. In this talk\, we discuss thes
e issues and how they are naturally connected to convexity of the variatio
nal integral on the underlying Dirichlet classes.\n\nThe talk is based on
joint work with Judith Campos Cordero\, Bernd Kirchheim and Jan Kolar.\n\n
The Passcode to the recorded video is: \nUcH03YU!\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Agostina Vivaldi (SAPIENZA” UNIVERSITA DI ROMA)
DTSTART:20210304T130000Z
DTEND:20210304T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/11
DESCRIPTION:Title: SAND PILES MODELS AND NON-LINEAR DIFFUSION EQUATIO
NS\nby Maria Agostina Vivaldi (SAPIENZA” UNIVERSITA DI ROMA) as pa
rt of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics
\n\n\nAbstract\nIn this talk\, we deal with theoretical and numerical aspe
cts of evolution and\ntime behavior of solutions to nonlinear diffusion eq
uations describing the dynamics of\nself-organizing sandpile process with
the critical state.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Hideo Kozono (Waseda University\, Tokyo)
DTSTART:20210311T130000Z
DTEND:20210311T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/12
DESCRIPTION:Title: Lr-Helmholtz-Weyl decomposition in two dimensional
exterior domains\nby Professor Hideo Kozono (Waseda University\, Toky
o) as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid m
echanics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Andrea Cianchi (University of Florence)
DTSTART:20210318T130000Z
DTEND:20210318T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/13
DESCRIPTION:Title: Symmetric gradient Orlicz-Sobolev spaces\nby P
rofessor Andrea Cianchi (University of Florence) as part of Fudan Internat
ional Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nA un
ified approach to embedding theorems for Sobolev type spaces of vector-val
ued functions\, defined via their symmetric gradient\, is proposed. The So
bolev spaces in question are built upon general rearrangement-invariant no
rms. Optimal target spaces in the relevant embeddings are determined withi
n the class of all rearrangement-invariant spaces. In particular\, all sym
metric gradient Sobolev embeddings into rearrangement-invariant target spa
ces are shown to be equivalent to the corresponding embeddings for the ful
l gradient built upon the same spaces. A sharp condition for embeddings in
to spaces of uniformly continuous functions\, and their optimal targets\,
are also exhibited. By contrast\, these embeddings may be weaker than the
corresponding ones for the full gradient. Related results\, of independent
interest in the theory of symmetric gradient Sobolev spaces\, are establi
shed. They include global approximation and extension theorems under minim
al assumptions on the domain. A formula for the K-functional\, which is pi
votal for our method based on a reduction to one-dimensional inequalities\
, is provided as well. The case of symmetric gradient Orlicz-Sobolev space
s\, of use in mathematical models in continuum mechanics driven by nonline
arities of non-power type\, is especially focused. This is joint work with
Dominic Breit.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics
of Siberian Branch of the Russian Academy of Sciences\, Novosibirsk\, Russ
ia)
DTSTART:20210408T130000Z
DTEND:20210408T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/14
DESCRIPTION:Title: Concentrations and singularities of solutions to t
he Navier-Stokes equations of compressible isentropic flows\nby Profes
sor Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics of Siberian Br
anch of the Russian Academy of Sciences\, Novosibirsk\, Russia) as part of
Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\
nAbstract\nAbstract. The talk is devoted to the theory of weak solutions t
o compressible Navier-Stokes equation with critical and subcritical adiaba
tic constants. In 2001\, Feireisl\, Novotny\, and Petzeltova proved the ex
istence of globally defined weak solutions to the Navier-Stokes equations
of compressible isentropic flows in the three space dimension on condition
that the adiabatic constant is greater than critical value 3/2. The cri
tical and subcritical cases are still poor investigated. The main difficul
ty lies in the fact that in the critical and subcritical cases\, the finit
e energy can be concentrated on sets of arbitrarily small measure. This le
ads to the so-called concentration problem. In the present work\, we prove
the absence of concentrations of the kinetic energy tensor in the critica
l case. We also give the derivation of estimates of non-stationary potenti
als of the pressure function. These estimates allow us to estimate from be
low the Hausdorff dimension of the support of the concentrations-defect me
asure. The case of rotationally symmetric solutions with adiabaticconstant
equals 1 is studied in details. In this case we prove that the concentra
tions-defect measure of the kinetic energy tensor is a matrix-valued measu
re\, which is concentrated on the symmetry axis and depends only on the ti
me variable. In particular\, the divergence of the concentrations-defect m
easure equals zero.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiri Neustupa (nstitute of Mathematics\, The Czech Academy of Scie
nces\, Prague\, Czech Republic)
DTSTART:20210415T130000Z
DTEND:20210415T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/15
DESCRIPTION:Title: New regularity criteria for weak solutions to the
MHD equations in terms of an associated pressure\nby Jiri Neustupa (ns
titute of Mathematics\, The Czech Academy of Sciences\, Prague\, Czech Rep
ublic) as part of Fudan International Seminar on Analysis\, PDEs\, and Flu
id mechanics\n\n\nAbstract\nAssume that Omega is either a smooth bounded d
omain in R3 or Omega=R3\, and Omega' is a sub-domain of Omega. Our main th
eorem states that if 0 <= T1 < T2 <= T <= \\infty\, (u\,b\,p) is a suitabl
e weak solution of an initial-boundary value problem for the MHD equations
in Omega x (0\,T)\, and either p- (the negative part of p) or B+ (the pos
itive part of B:=p+|u|^2+|b|^2) satisfy certain new a posteriori condition
s in Omega' x (T1\,T2) then the solution has no singular points in Omega'
x (T1\,T2). If b=0 then our theorem generalizes some known results from th
e theory of the Navier-Stokes equations. We give a comparison with previou
s related results and show the principles of the proof. The talk is based
on a joint paper with Minsuk Yang\, Yonsei University\, Seoul.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Toshiaki Hishida (Nagoya University\, Japan)
DTSTART:20210422T130000Z
DTEND:20210422T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/16
DESCRIPTION:Title: Optimal boundary control for steady motions of a s
elf-propelled body in a viscous incompressible fluid\nby Professor Tos
hiaki Hishida (Nagoya University\, Japan) as part of Fudan International S
eminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nConsider st
eady motions of a self-propelled rigid body into an infinite viscous incom
pressible fluid in 3D. We say that a body undergoes a self-propelled motio
n if the external force and external torque acting on fluid-body are zero
so that the body moves only by a mechanism produced by itself at the bound
ary through fluid-body interaction. Given translational and angular veloci
ties being assumed to be small\, we show the existence of many boundary co
ntrols subject to a physically relevant side condition (such as tangential
control or localized control) which generate the self-propelled motionof
the body with target velocity and then discuss minimizationof the work to
overcome the drag. We next derive a necessary condition for optimal bounda
ry control in terms of a variational inequality\, where the adjoint state
associated\nwith the optimal control is involved as a Lagrange multiplier.
This talk is based on a joint work with Ana Silvestre (Lisbon) and Takeo
Takahashi (Nancy).\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Antonin Novotny (University of Toulon\, IMATH\, France)
DTSTART:20210429T130000Z
DTEND:20210429T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/17
DESCRIPTION:Title: On the weak solvability of some compressible bi-fl
uid models with general in/out-flow boundary data\nby Professor Antoni
n Novotny (University of Toulon\, IMATH\, France) as part of Fudan Interna
tional Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe
will discuss the existence of weak solutions for some simple models of mix
tures of several compressible viscous and noninteracting fluids. A particu
lar attention in this talk will be devoted to the explanation of the role
played by the pure transport and continuity equations in the existence pro
of.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Eduard Feireisl (Institute of Mathematics of the Academy
of Sciences of the Czech Republic\; Institute of Mathematics\, Technische
Universitat Berlin)
DTSTART:20210506T130000Z
DTEND:20210506T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/18
DESCRIPTION:Title: Obstacle problem\, Euler system\, and turbulence\nby Professor Eduard Feireisl (Institute of Mathematics of the Academy
of Sciences of the Czech Republic\; Institute of Mathematics\, Technische
Universitat Berlin) as part of Fudan International Seminar on Analysis\, P
DEs\, and Fluid mechanics\n\n\nAbstract\nWe consider a statistical limit o
f solutions to the compressible Navier-Stokes system in the high Reynolds
number regime in a domain exterior to a rigid body. We investigate to what
extent this highly turbulent regime can be modeled by an external stochas
tic perturbation\, as suggested in the related physics literature.\nTo thi
s end\, we interpret the statistical limit as a stochastic process on the
associated trajectory space. We suppose that the limit process is statisti
cally equivalent to a solution of the stochastic compressible Euler system
. Then\, necessarily\,\n(a) the stochastic forcing is not active - the lim
it is a statistical solution of the deterministic Euler system\;\n(b) the
solutions S-converge to the limit\;\n(c) if\, in addition\, the expected v
alue of the limit process solves the Euler system\, then the limit is dete
rministic and the convergence is strong in the L^p-sense.\n \nThese result
s strongly indicate that a stochastic forcing may not be a suitable model
for turbulent randomness in compressible fluid flows.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao Ren (Fudan University)
DTSTART:20210513T130000Z
DTEND:20210513T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/19
DESCRIPTION:Title: Leray's plane stationary solutions have the prescr
ibed limit at infinity in the case of small Reynolds numbers\nby Xiao
Ren (Fudan University) as part of Fudan International Seminar on Analysis\
, PDEs\, and Fluid mechanics\n\n\nAbstract\nIn the celebrated 1933 paper\,
J. Leray proposed the invading domains method to construct D-solutions fo
r the stationary Navier-Stokes flow around obstacle problem. In two dimens
ions\, whether Leray's D-solution achieves the prescribed limiting velocit
y at spatial infinity became a major open problem since then. In this pape
r\, we solve this problem at small Reynolds numbers. The proof builds on a
novel blow-down argument which rescales the invading domains to the unit
disc\, and the ideas developed in a recent paper [Korobkov-Pileckas-Russo2
020]\, where the nontriviality of Leray solutions in the general case was
proved\, and [Korobkov-Ren-2021]\, where the uniqueness result for small R
eynolds number was established. The talk is based on a joint work with M.K
orobkov\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Guillod (Sorbonne University (France))
DTSTART:20210520T130000Z
DTEND:20210520T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/20
DESCRIPTION:Title: Stationary Navier–Stokes equations in the plane<
/a>\nby Julien Guillod (Sorbonne University (France)) as part of Fudan Int
ernational Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\
nThe aim of this talk is to review the current knowledge on the steady sol
utions of the Navier–Stokes equations in the whole two-dimensional plane
. This case is more difficult than the three-dimensional space for some re
asons that will be discussed. In the first part\, I will discuss the const
ruction of weak solutions through topological methods\, and in the second
part how the scaling invariance can be used to construct perturbative solu
tions. I will mainly focus on the open problems and introduce some numeric
al results and conjectures.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Yasunori Maekawa (Kyoto University)
DTSTART:20210527T130000Z
DTEND:20210527T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/21
DESCRIPTION:Title: Gevrey stability of Rayleigh boundary layer in the
inviscid limit\nby Professor Yasunori Maekawa (Kyoto University) as p
art of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanic
s\n\n\nAbstract\nWe will show the Prandtl boundary layer expansion for the
two-dimensional Navier-Stokes flows around the Rayleigh boundary layer\,
which verifies the stability of the formation of the boundary layer in the
inviscid limit with respect to the perturbations in the Gevrey 3/2 class.
\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Ping Zhang (Kyoto University)
DTSTART:20210603T130000Z
DTEND:20210603T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/22
DESCRIPTION:Title: Global existence and decay of solutions to Prandtl
system with small analytic and Gevrey data\nby Professor Ping Zhang (
Kyoto University) as part of Fudan International Seminar on Analysis\, PDE
s\, and Fluid mechanics\n\n\nAbstract\nIn this talk\, we prove the global
existence and the large time decay estimate of solutions to the Prandtl sy
stem with small initial data\, which is analytical in the tangential varia
ble.\n\nThe key ingredient used in the proof is to derive a sufficiently f
ast decay-in-time estimate of some weighted analytic energy estimate to a
quantity\, which consists of a linear combination of the tangential veloci
ty with its primitive one\, and which basically controls the evolution of
the analytical radius to the solutions. Our result can be viewed as a glob
al-in-time Cauchy-Kowalevsakya result for the Prandtl system with small an
alytical data\, which in particular improves the previous result in \\cite
{IV16} concerning the almost global well-posedness of the two-dimensional
Prandtl system. Finally\, I'll present our recent result concerning the gl
obal well-posedness with small Gevrey data. This is partially joint work w
ith N. Liu\; M. Paicu\; C. Wang and Y. Wang.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Anvarbek Meirmanov (National Research University "Higher
School of Economics"\, Moscow\, Russia)
DTSTART:20210325T130000Z
DTEND:20210325T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/23
DESCRIPTION:Title: Mathematical models of oil reservoir\nby Profe
ssor Anvarbek Meirmanov (National Research University "Higher School of Ec
onomics"\, Moscow\, Russia) as part of Fudan International Seminar on Anal
ysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nThis report is devoted to
mathematical models of displacement of oil by some suspension in rocks du
ring oil production. Mathematical models of the oil reservoir are very imp
ortant from both theoretical and practical points of view. So far\, one of
the most popular such models is the Backley-Leverett model. (1) Probably
\, the next known model could be the Muskat problem. (2) Each of these mod
els is a phenomenological mathematical model. That is\, it describes the p
hysical process at the macroscopic level\, where the characteristic size o
f the domain under consideration is several meters. We discuss existing ph
enomenological models of oil reservoir and suggest new exact mathematical
models based on ideas R. Barridge and J. Keller (3) and E. Sanchez-Palenci
a (4) (mathematical modelling) and G. Nguetseng (5) (homogenization). Fina
lly\, we illustrate our results with some numerical implementations for on
e-porosity geometries and compare obtained results for different mathemati
cal models.\n\n1. S.E. Buckley and M.C. Leverett\, 1942\, Mechanism o
f fluid displacements in sands\, Transactions of the AIME\, v.146\, pp. 10
7-116.\n2. M. Muskat\, Two fluid systems in porous media. The encroach
ment of water into an oil sand\, Physics\, 5\, 1934.\n3. R. Barridge a
nd J. Keller\, Poroelasticity equations derived from microstructure\, J. A
coust. Soc. Am.\, V. 70\, issue 4\, 1981.\n4. E. Sanchez-Palencia\, No
n-homogeneous media and vibration theory\, Lecture Notes in Phys.\, 127\,
Springer-Verlag\, Berlin–New York\, 1980.\n5. G. Nguetseng\, A gener
al convergence result for a functional related to the theory of homogeniza
tion\, SIAM J. Math. Anal.\, V. 20\, issue 3\, 1989\, 608 - 623.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Grigory Seregin (Oxford University and St. Petersburg Instit
ute of Mathematics)
DTSTART:20211014T130000Z
DTEND:20211014T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/24
DESCRIPTION:Title: A Slightly Supercritical Condition of Regularity o
f Axisymmetric Solutions to the Navier-Stokes Equations\nby Prof. Grig
ory Seregin (Oxford University and St. Petersburg Institute of Mathematics
) as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid me
chanics\n\n\nAbstract\nIn the talk\, a new regularity condition for axisym
metric solutions to the non-stationary 3D Navier-Stokes equations is discu
ssed. It is slightly supercritical.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Yosef Yomdin (The Weizmann Institute of Science\, Rehovot\,
Israel)
DTSTART:20211104T130000Z
DTEND:20211104T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/26
DESCRIPTION:Title: Estimating high order derivatives of a function th
rough geometry and topology of its zero set\nby Prof. Yosef Yomdin (Th
e Weizmann Institute of Science\, Rehovot\, Israel) as part of Fudan Inter
national Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nW
e study a very special setting of the Whitney smooth extension problem: fo
r a given closed subset Z in the ball B^n\, we consider normalized (d+1)-s
mooth functions f on B^n\, vanishing on Z\, and ask for the minimal possib
le norm ||f^(d+1)|| of their last derivative. We discuss some recent resu
lts in this direction\, which use as an input the ``density’’ of Z\, o
r\, in contrast\, its topology. In particular\, the role of the density o
f Z is analyzed via Remez-type inequalities\, on one side\, and via restri
ction to smooth curves\, on the other side.\n\n In order to incorporate to
pological information on Z\, we use\, in particular\, some recent results
of Lerario and Stecconi\, comparing topology of smooth transversal singula
rities\, and of their polynomial approximations. If time allows\, we plan
also to present the lower bounds on the minimal possible norm ||f^(d+1)||\
, given the set of critical values of f.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Andrej Zlatos (University of California\, San Diego\, US
A)
DTSTART:20211118T130000Z
DTEND:20211118T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/27
DESCRIPTION:Title: Euler Equations on General Planar Domains\nby
Professor Andrej Zlatos (University of California\, San Diego\, USA) as pa
rt of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics
\n\n\nAbstract\nBounded vorticity solutions to the 2D Euler equations on s
ingular domains are typically not close to Lipschitz near boundary singula
rities\, which makes their uniqueness a difficult open problem. I will pre
sent a general sufficient condition on the geometry of the domain that gua
rantees global uniqueness for all solutions initially constant near the bo
undary. This condition is only slightly more restrictive than exclusion of
corners with angles greater than $\\pi$ and\, in particular\, is satisfie
d by all convex domains. Its proof is based on showing that fluid particle
trajectories for general bounded vorticity solutions cannot reach the bou
ndary in finite time. The condition also turns out to be sharp in the latt
er sense: there are domains that come arbitrarily close to satisfying it a
nd on which particle trajectories can reach the boundary in finite time.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Semyon Dyatlov (Massachusetts Institute of Technology\,
USA)
DTSTART:20211216T130000Z
DTEND:20211216T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/28
DESCRIPTION:Title: Quantum chaos: advances and perspectives\nby P
rofessor Semyon Dyatlov (Massachusetts Institute of Technology\, USA) as p
art of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanic
s\n\n\nAbstract\nWhere do eigenfunctions of the Laplacian concentrate as e
igenvalues go to infinity? Do they equidistribute or do they concentrate i
n an uneven way? It turns out that the answer depends on the nature of the
geodesic flow. I will discuss various results in the case when the flow i
s chaotic: the Quantum Ergodicity theorem of Shnirelman\, Colin de Verdi\\
`ere\, and Zelditch\, the Quantum Unique Ergodicity conjecture of Rudnick-
-Sarnak\, the progress on it by Lindenstrauss and Soundararajan\, and the
entropy bounds of Anantharaman--Nonnenmacher. I will conclude with a more
recent lower bound on the mass of eigenfunctions obtained with Jin and Non
nenmacher. It relies on a new tool called "fractal uncertainty principle"
developed in the works with Bourgain and Zahl.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Igor Pazanin (University of Zagreb\, Croatia)
DTSTART:20220113T130000Z
DTEND:20220113T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/29
DESCRIPTION:Title: The effective boundary condition on a porous wall<
/a>\nby Professor Igor Pazanin (University of Zagreb\, Croatia) as part of
Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\
nAbstract\nThe aim of this talk is to present the derivation of the new ef
fective boundary condition for the fluid flow in a domain with porous boun
dary. Starting from the Stokes system in a domain with an array of small h
oles on the boundary and using the homogenization and the boundary layers\
, we find an effective law in the form of generalized Darcy law. If the po
res geometry is isotropic\, then the condition splits in Beavers-Joseph ty
pe condition for the tangential flow and the standard Darcy condition for
the normal flow. In the second part of the talk\, we study the roughness-i
nduced effects on the proposed Darcy-type boundary condition.\n\nThe talk
is based on the joint work with Eduard Marusic-Paloka.\n\nPasscode for the
Recorded video link: c=q5RuW0\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Alexander Nazarov (St. Petersburg Department of Steklov
Institute of Mathematics (POMI) and St. Petersburg State University\, Rus
sia)
DTSTART:20220127T130000Z
DTEND:20220127T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/30
DESCRIPTION:Title: The Hopf-Oleinik Lemma for the divergence-type equ
ations\nby Professor Alexander Nazarov (St. Petersburg Department of
Steklov Institute of Mathematics (POMI) and St. Petersburg State Universit
y\, Russia) as part of Fudan International Seminar on Analysis\, PDEs\, an
d Fluid mechanics\n\n\nAbstract\nThe Hopf-Oleinik lemma\, known also as th
e “normal derivative lemma”\, is one of the important tools in qualita
tive analysis of partial differential equations.This lemma states that a s
upersolution of a partial differential equation with a minimum value at a
boundary point\, must increase linearly away from its boundary minimum pro
vided the boundary is smooth enough. A major part of all known results on
the normal derivative lemma concerns equations with nondivergence structur
e and strong solutions (see [1] and [2] for some recent results and the co
mprehensive historical review). \n\n The case of the divergence-type equat
ions is less studied. It is well known that the normal derivative lemma fa
ils for uniformly elliptic equations in divergence form with bounded and e
ven continuous leading coefficients. Thus\, one has to require more smooth
ness of the leading coefficients. \n\nFor the parabolic divergence-type eq
uations\, the normal derivative lemma can be also extracted from the lower
bound estimates of the Green function for the corresponding operator.\n\n
We present a version of the Hopf-Oleinik lemma for general elliptic and pa
rabolic equations in divergence form under the sharp requirements on the c
oefficients of equations and on the boundary of a domain. All our assumpti
ons are significantly weakened in comparison with the previous works. In f
act\, our requirements are close to the necessary ones. The talk is based
on the paper [3]. \n\nReferences\n\n[1] A.I. Nazarov\, A centennial of the
Zaremba-Hopf-Oleinik lemma\, SIAM J. Math. Anal. 44(2012)\, no. 1\, 437
–453.\n\n[2] D.E. Apushkinskaya\, A.I. Nazarov\, A counterexample to the
Hopf-Oleinik lemma (elliptic case)\, Anal. PDE 9(2016)\, no. 2\, 439–45
8.\n\n[3] D.E. Apushkinskaya\, A.I. Nazarov\, On the Boundary Point Princi
ple fordivergence-type equations\, Rend. Lincei Mat. Appl. 30(2019)\, 677
–699.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao Ren (Fudan university\, Shanghai\, China)
DTSTART:20220224T130000Z
DTEND:20220224T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/31
DESCRIPTION:Title: Existence and uniqueness for plane stationary Navi
er–Stokes flows with compactly supported force\nby Xiao Ren (Fudan u
niversity\, Shanghai\, China) as part of Fudan International Seminar on An
alysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe prove two basic esti
mates for 2D stationary Navier-Stokes solutions\, which have rather simple
forms. Then\, we apply them to the stationary Navier–Stokes equations i
n the whole plane with an external force and with a prescribed constant sp
atial limit. Using the first estimate\, we solve the key difficulties in a
pplying Leray’s invading domains method in the whole plane and\, as a co
nsequence\, prove the existence of stationary Navier-Stokes D-solutions wi
th arbitrary compactly supported force. Using the second estimate\, we ver
ify the boundary condition at infinity in two different scenarios: (I) the
limit velocity is sufficiently large with respect to the external force\,
(II) both the total integral of force and the limit velocity vanish. Henc
e\, our method produces large class of new solutions with prescribed spati
al limits. We also show the uniqueness of D-solutions to the forced proble
m in a perturbative regime. \nThe talk is based on the recent joint paper
with Julien Guillod (Sorbonne Universite) and Mikhail Korobkov\, see https
://arxiv.org/abs/2111.11042\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor David Gomes-Castro (University of Oxford)
DTSTART:20220310T130000Z
DTEND:20220310T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/32
DESCRIPTION:Title: Concentration phenomena in Aggregation-Diffusion E
quations\nby Professor David Gomes-Castro (University of Oxford) as p
art of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanic
s\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Giovanni Paolo Galdi (University of Pittsburgh\, USA)
DTSTART:20220324T130000Z
DTEND:20220324T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/33
DESCRIPTION:Title: Navier-Stokes Equations around a Rigid Body: Three
Remarkable Open Problems\nby Professor Giovanni Paolo Galdi (Universi
ty of Pittsburgh\, USA) as part of Fudan International Seminar on Analysis
\, PDEs\, and Fluid mechanics\n\n\nAbstract\nThe motion of a (finite) rigi
d body\, B\, in a viscous liquid is a fundamental and widely investigated
problem of mathematical fluid mechanics\, in both cases when the motion of
B is either prescribed or it becomes part of the problem. However\, in sp
ite of the many outstanding contributions tracing back to the works of Ler
ay\, Ladyzhenskaya and Finn\, there is still a plethora of fundamental que
stions that remain still unanswered and call for the attention of the inte
rested mathematician. Objective of this talk is to present and discuss thr
ee among the most remarkable ones.\n\nPasscode for the video-link: EeGU5+k
7\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Timofey Shilkin (St.-Petersburg Branch of V.A. Steklov I
nstitute of Mathematics)
DTSTART:20220407T130000Z
DTEND:20220407T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/34
DESCRIPTION:Title: Surprising properties of weak solutions to ellipti
c equations with a singular drift\nby Professor Timofey Shilkin (St.-P
etersburg Branch of V.A. Steklov Institute of Mathematics) as part of Fuda
n International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbst
ract\nWe study properties of weak solutions to the Dirichlet problem for s
calar elliptic equations of the convection-diffusion type. It is well-know
n that in the case of a regular drift (which is not necessarily divergence
-free) weak solutions possess a set of properties which are typical in the
elliptic theory. In this talk we will follow how the properties of weak s
olutions change in the case when the drift has limited smoothness.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Dallas Albritton (Institute for Advanced Study\, USA)
DTSTART:20220421T130000Z
DTEND:20220421T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/35
DESCRIPTION:Title: Non-uniqueness of Leray solutions of the forced Na
vier-Stokes equations\nby Professor Dallas Albritton (Institute for Ad
vanced Study\, USA) as part of Fudan International Seminar on Analysis\, P
DEs\, and Fluid mechanics\n\n\nAbstract\nIn a seminal work\, Leray demonst
rated the existence of global weak solutions to the Navier-Stokes equation
s in three dimensions. Are Leray's solutions unique? This is a fundamental
question in mathematical hydrodynamics\, which we answer in the negative\
, within the `forced' category\, by exhibiting two distinct Leray solution
s with zero initial velocity and identical body force. This is joint work
with Elia Brué and Maria Colombo.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Filippo Gazzola (The Polytechnic University of Milan)
DTSTART:20220428T130000Z
DTEND:20220428T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/36
DESCRIPTION:Title: Long-time behavior of partially damped systems mod
eling degenerate plates with piers\nby Professor Filippo Gazzola (The
Polytechnic University of Milan) as part of Fudan International Seminar on
Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe consider a partia
lly damped nonlinear beam-wave system of evolution PDE's modeling the dyna
mics of a degenerate plate. The plate can move both vertically and torsion
ally and\, consequently\, the solution has two components. We show that th
e component from the damped beam equation always vanishes asymptotically w
hile the component from the (undamped) wave equation does not. In case of
small energies we show that the first component vanishes at exponential ra
te. Our results highlight that partial damping is not enough to steer the
whole solution to rest and that the partially damped system can be less st
able than the undamped system. Hence\, the model and the behavior of the s
olution enter in the framework of the so-called "indirect damping" and "de
stabilization paradox". These phenomena are valorized by a physical interp
retation leading to possible new explanations of the Tacoma Narrows Bridge
collapse.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Tobias Barker (University of Bath\, UK)
DTSTART:20220505T130000Z
DTEND:20220505T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/37
DESCRIPTION:Title: Failure of Liouville type theorems and potential '
type I' singularities of the Navier-Stokes equations\nby Professor Tob
ias Barker (University of Bath\, UK) as part of Fudan International Semina
r on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nIt is known that
if a solution of the 3D Navier-Stokes equations loses smoothness\, then t
here necessarily exists a non-zero bounded solution defined on the whole b
ackward time interval. \nIn this talk\, I will focus on the reverse impli
cation. \nJoint work with Dallas Albritton (IAS).\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Gisella Croce (Laboratoire de Mathematiques Appliquees d
u Havre)
DTSTART:20220519T130000Z
DTEND:20220519T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/38
DESCRIPTION:Title: On the quantitative isoperimetric inequality in th
e plane\nby Professor Gisella Croce (Laboratoire de Mathematiques Appl
iquees du Havre) as part of Fudan International Seminar on Analysis\, PDEs
\, and Fluid mechanics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Anvar Meirmanov (Moscow State University of Civil Engine
ering\, Moscow)
DTSTART:20220602T130000Z
DTEND:20220602T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/39
DESCRIPTION:Title: On the classical solution to the macroscopic model
for in-situ leaching of rare metals\nby Professor Anvar Meirmanov (Mo
scow State University of Civil Engineering\, Moscow) as part of Fudan Inte
rnational Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\n
We consider initial boundary value problems arising in mathematical models
for in -- situ leaching of rare metals or for cleaning the bottom-hole zo
ne of oil wells with\ndouble - porosity structure and special periodicity.
\nFirst\, we consider this physical process at the microscopic level (the
characteristic pore size is approximately 5-20 microns\, governed by Lame
equations for the solid skeleton\, the Stokes equations for the liquid co
mponent\, and the diffusion-convection equations for concentrations of aci
d and products of a chemical reaction. \nDue to its dissolution\, the soli
d skeleton has an unknown (free) boundary with the pore and cavity spaces.
\nNext\, assuming the existence of a generalized solution to the correspo
nding initial-boundary value problem at the microscopic level and using th
e homogenization method together with the fixed point theorem\, we derive
the Bio's model describing the physical process of in-situ leaching for sl
ightly viscous liquid in the double - porosity elastic solid skeleton at t
he macroscopic level.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Piotr Hajłasz (University of Pittsburgh\, USA)
DTSTART:20221020T130000Z
DTEND:20221020T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/40
DESCRIPTION:Title: Approximation of mappings with derivatives of low
rank\nby Professor Piotr Hajłasz (University of Pittsburgh\, USA) as
part of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechani
cs\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Stefano Modena (Gran Sasso Science Institute (GSSI)\, It
aly)
DTSTART:20221103T130000Z
DTEND:20221103T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/41
DESCRIPTION:Title: Non-uniqueness for the transport equation with Sob
olev vector fields\nby Professor Stefano Modena (Gran Sasso Science In
stitute (GSSI)\, Italy) as part of Fudan International Seminar on Analysis
\, PDEs\, and Fluid mechanics\n\n\nAbstract\nOne of the main questions in
the theory of the linear transport equation is whether uniqueness of weak
solutions to the Cauchy problem holds in the case the given vector field i
s not smooth. In the talk I will provide an overview on some results obtai
ned in the last few years\, showing that even for incompressible\, Sobolev
(thus quite ``well-behaved") vector fields\, uniqueness of solutions can
drastically fail. This result can be seen as a counterpart to DiPerna and
Lions' well-posedness theorem.\n\nPasscode for the video-link:S*9@4C#H\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics\,
Novosibirsk)
DTSTART:20221117T130000Z
DTEND:20221117T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/42
DESCRIPTION:Title: Isothermal coordinates on surfaces with a square-i
ntegrable second fundamental form. Existence and counterexamples\nby P
rofessor Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics\, Novosibi
rsk) as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid
mechanics\n\n\nAbstract\nThe question of the existence of isothermal coor
dinates on two-dimensional surfaces goes back to the work of Gauss on diff
erential geometry. The first nonlocal theorem on the existence of isotherm
al coordinates for quadratic differential forms with smooth coefficients w
as proved by Lichtenstein (1916). For forms with bounded coefficients this
result was established by Morrey(1938). Morrey's theorem has been repeate
dly reproved and refined. In modern literature\, it is often referred to a
s the Ahlfors-Bers-Bojarski-Morrey theorem. Here we should also mention th
e result of Helein (2002) on the existence isothermal coordinates for diff
erential quadratic forms with Sobolev coefficients.\n For many applicat
ions\, it is important to find isothermal coordinates with a uniformly bou
nded conformal factor logarithm. Such coordinates are called bi-Lipschitz
coordinates. The existence of bi-Lipschitz coordinates is an essential ing
redient of the mathematical theory of biological membranes. In 1994 Toro
proved the remarkable theorem on the existence of bi-Lipschitz isothermal
coordinates for surfaces with a square-integrable second fundamental form.
It should be noted that her approach is based on the theory of varifolds
and geometric measure theory. An analytical approach to the problem was p
roposed in the works of Kuwert and Li\, and Riviera (2012). They introduc
ed a class of weak immersions with a square-integrable second fundamental
form. An immersion of a two-dimensional closed manifold into a Euclidean s
pace belongs to this class if its first fundamental form is uniformly boun
ded above and below\, and its second fundamental form is square integrable
.\n A common belief is the existence of bi-Lipschitz isothermal coordi
nates for all such immersions. This fact is widely used in the mathematica
l theory of biological membranes. In the proposed work\, we show that this
assertion is not true in the general case. We give an example of weak imm
ersion of a two-dimensional sphere for which there are no bi-Lipschitz iso
thermal coordinates. On the other hand\, we prove the existence of such co
ordinates for all weak immersions of tori. The connection of these results
with Teichmüller's theory is discussed. Our approach is based on the Che
rn-Helein moving frame method and the Moser-Struwe result on the validity
of the Liouville theorem for elliptic equations with bounded periodic coef
ficients.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Eduard Marušić-Paloka (University of Zagreb\, Croatia)
DTSTART:20221201T130000Z
DTEND:20221201T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/43
DESCRIPTION:Title: Mathematical model of heat transfer through a cond
uctive pipe\nby Professor Eduard Marušić-Paloka (University of Zagre
b\, Croatia) as part of Fudan International Seminar on Analysis\, PDEs\, a
nd Fluid mechanics\n\n\nAbstract\nThe standard engineer's model for heat t
ransfer between the fluid flowing through the pipe and the exterior medium
neglects the effects of the pipe's wall. The goal of this paper is to pro
ve that they are not always negligible. Comparing the ratio between diffus
ivities of the fluid and the wall with the wall's thickness\, using rigoro
us asymptotic analysis\, we find five different models for effective descr
iption of the heat exchange process.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Piotr B Mucha (University of Warsaw\, Poland)
DTSTART:20221215T130000Z
DTEND:20221215T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/44
DESCRIPTION:Title: A new construction of weak solutions to compressib
le Navier-Stokes equations\nby Professor Piotr B Mucha (University of
Warsaw\, Poland) as part of Fudan International Seminar on Analysis\, PDEs
\, and Fluid mechanics\n\n\nAbstract\nI plan to talk about the existence o
f the weak solutions to the compressible Navier--Stokes system with barotr
opic pressure for $\\gamma \\geq 9/5$ in three dimension. The novelty of t
he paper is the approximation scheme that instead of the classical regular
ization of the continuity equation (based on the viscosity approximation $
\\epsilon \\Delta$) uses more direct truncation and regularisation of non
linear terms an the pressure. This scheme is compatible with the Bresch-J
abin compactness criterion for the density. We revisit this criterion and
prove\, in full rigour\, that it can be applied in our approximation at a
ny level.\n\nBased on: Nilasis Chaudhuri\, Piotr B. Mucha\, Ewelina Zators
ka -- arXiv:2211.12189\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Patrick Tolksdorf (Johannes Gutenberg-Universität Mainz
\, Germany)
DTSTART:20230105T130000Z
DTEND:20230105T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/45
DESCRIPTION:Title: L^p-extrapolation of the generalized Stokes operat
or\nby Professor Patrick Tolksdorf (Johannes Gutenberg-Universität Ma
inz\, Germany) as part of Fudan International Seminar on Analysis\, PDEs\,
and Fluid mechanics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Reinhard Farwig (Technische Universität Darmstadt\, Dar
mstadt\, Germany)
DTSTART:20230119T130000Z
DTEND:20230119T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/46
DESCRIPTION:Title: The Navier-Stokes System with Moving Boundaries -
From Bounded to Unbounded Domains\nby Professor Reinhard Farwig (Techn
ische Universität Darmstadt\, Darmstadt\, Germany) as part of Fudan Inter
national Seminar on Analysis\, PDEs\, and Fluid mechanics\n\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Vincenzo Ferone (Università degli Studi di Napoli Feder
ico II\, Naples\, Italy)
DTSTART:20230223T130000Z
DTEND:20230223T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/47
DESCRIPTION:Title: Symmetrization for linear and nonlinear fractional
elliptic problems\nby Professor Vincenzo Ferone (Università degli St
udi di Napoli Federico II\, Naples\, Italy) as part of Fudan International
Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe descri
be symmetrization results in the form of mass concentration (i.e. integral
) comparison for fractional elliptic equations involving the s-laplacian (
0 < s < 1). We use a new direct method which recovers\, in the limit as s
goes to 1\, the classical pointwise Talenti rearrangement inequality. Some
possible applications of the method to nonlinear equations and to equatio
ns with lower order terms will be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Milan Pokorný (Charles University\, Prague\, Czech Repu
blic)
DTSTART:20230309T130000Z
DTEND:20230309T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/48
DESCRIPTION:Title: Homogenization of Navier-Stokes-Fourier system in
domains with tiny holes\nby Professor Milan Pokorný (Charles Universi
ty\, Prague\, Czech Republic) as part of Fudan International Seminar on An
alysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe consider the compres
sible Navier–Stokes–Fourier system in a domain with large\nnumber of h
oles. Under the assumption that the holes are sufficiently small\, togethe
r\nwith certain standard assumptions on the adiabatic exponent and the beh
aviour of the\nheat conductivity\, we show that if passing simultaneously
with the number of holes to\ninfinity and their size to zero\, in the limi
t we obtain again a solution to the compressible\nNavier–Stokes–Fourie
r system in the domain without holes. The result holds both for\nthe stead
y and evolutionary problem. The talk is based on a paper with Yong Lu\n(Na
njing University)\, a paper with Emil Skˇr´ıˇsovsk´y (Charles Univers
ity\, Prague) and\nrecent results obtained together with F. Oschmann (Math
ematical Institute of the Czech\nAcademy of Sciences).\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Vladimír Šverák (University of Minnesota)
DTSTART:20230420T130000Z
DTEND:20230420T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/49
DESCRIPTION:Title: On the motion of vortex rings in low viscosity flu
ids\nby Professor Vladimír Šverák (University of Minnesota) as part
of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n
\n\nAbstract\nWe will discuss the Cauchy problem for the 3d Navier-Stokes
equation in which the initial vorticity represents an idealized current of
a (possibly large) given strength supported on a circle. A detailed descr
iption of the behavior of the solution in the regime of very low viscosity
will be given. This is joint work with Thierry Gallay.\n\nThe passcode fo
r the Recorded video link:\nP5@UVfn$\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Andrea Cianchi (University of Florence)
DTSTART:20230504T130000Z
DTEND:20230504T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/50
DESCRIPTION:Title: Distortion of Hausdorff measures under Orlicz-Sobo
lev maps\nby Professor Andrea Cianchi (University of Florence) as part
of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n
\n\nAbstract\nA comprehensive theory of the effect of Orlicz-Sobolev maps\
, between Euclidean spaces\, on subsets with zero or finite Hausdorff meas
ure is offered. Arbitrary Orlicz-Sobolev spaces embedded into the space of
continuous function and Hausdorff measures built upon general gauge funct
ions are included in our discussion. An explicit formula for the distortio
n of the relevant gauge function under the action of these maps is exhibit
ed in terms of the Young function defining the Orlicz-Sobolev space. New p
henomena and features\, related to the flexibility in the definition of th
e degree of integrability of weak derivatives of maps and the notion of me
asure of sets\, are detected. Classical results\, dealing with standard So
bolev spaces and Hausdorff measures\, are recovered\, and their optimality
is shown to hold in a refined stronger sense. Special instances available
in the literature\, concerning Young functions and gauge functions of non
-power type\, are also reproduced and\, when not sharp\, improved. This is
joint work with M.V.Korobkov and J.Kristensen.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Grigory Panasenko (University Jean Monnet and Vilnius Un
iversity)
DTSTART:20230518T130000Z
DTEND:20230518T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/51
DESCRIPTION:Title: Asymptotic analysis and method of partial asymptot
ic dimension reduction for thin tube structures\nby Professor Grigory
Panasenko (University Jean Monnet and Vilnius University) as part of Fudan
International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstr
act\nThe talk briefly presents the results of asymptotic analysis for non-
Newtonian flows in thin tube structures (see G. Panasenko\, K.Pileckas\, a
nd B.Vernescu “Steady state non-Newtonian flow with strain rate dependen
t viscosity in thin tube structure with no slip boundary condition”\, Ma
thematical Modelling of Natural Phenomena 17\, 2022\, 36pp. www.mmnp-journ
al.org (open access)) and introduces the method of partial asymptotic dime
nsion reduction (PADRED) (see G. Panasenko\, K.Pileckas\, “Partial asymp
totic dimension reduction for steady state non-Newtonian flow with strain
rate dependent viscosity in thin tube structure”\, J.Math. Fluid. Mech.\
, 25:11\, 2023\, https://doi.org/10.1007/s00021-022-00749-5). The computat
ion of the leading term of the solution is related to the equation on the
graph\, which is an elliptic nonlinear problem. We introduce a numerical m
ethod to solve the equation on the graph and apply it to the realistic net
work of blood vessels.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Pier Domenico Lamberti (Universita' degli Studi di Padov
a)
DTSTART:20230601T130000Z
DTEND:20230601T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/52
DESCRIPTION:Title: Spectral representation of the trace spaces and th
e solutions of the Dirichlet biharmonic problem on Lipschitz domains via m
ulti-parameter Steklov problems\nby Professor Pier Domenico Lamberti (
Universita' degli Studi di Padova) as part of Fudan International Seminar
on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe consider the pr
oblem of describing the traces of functions in H^2 on the boundary of a Li
pschitz domain in the N-dimensional Euclidean space. We provide a definit
ion of those spaces\, in particular of H^{3/2} by means of Fourier series
associated with the eigenfunctions of new multi-parameter biharmonic Stekl
ov problems which we introduce with this specific purpose. These definitio
ns coincide with the classical ones when the domain is smooth. Our spaces
allow to represent in series the solutions to the biharmonic Dirichlet pro
blem. Based on joint work with Luigi Provenzano.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Chunjing Xie (Shanghai Jiao Tong University\, China)
DTSTART:20231214T130000Z
DTEND:20231214T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/53
DESCRIPTION:Title: The uniqueness and existence of steady solutions o
f incompressible Navier-Stokes system in a nozzle\nby Professor Chunji
ng Xie (Shanghai Jiao Tong University\, China) as part of Fudan Internatio
nal Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nA long
standing open problem for steady incompressible Navier-Stokes is the so ca
lled the Leray problem\, which aims to give the existence of steady flows
in an infinitely long nozzle with Poiseuille flows as far field behavior.
The problem was solved by Amick\, Ladyzhenskaya\, Solonnikov\, etc when th
e fluxes of the flows are small. When the flux is large\, the existence of
solutions to steady Navier-Stokes system was obtained by Ladyzhenskaya an
d Solonnikov. In order to completely solve the Leray problem\, we may need
to prove global uniqueness of Poiseuille flows in a straight cylinder. In
this talk\, we first address the recent progress on nonlinear structural
stability of Hagen-Poiseuille flows in a pipe\, in particular\, the unifor
m stability of these flows with respect to the mass flux\, where the key i
ngrident is the analysis of the associated linearized problem. Second\, we
prove the existence of the solutions in a channel when the flows satisfy
the Navier boundary conditions where the uniform local estimates play a cr
ucail role.\n\nPasscode for the videolink:\n67&LEYj.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Tai-Peng Tsai (The University of British Columbia\, Vanc
ouver\, Canada)
DTSTART:20230615T130000Z
DTEND:20230615T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/54
DESCRIPTION:Title: Gradient estimates for the non-stationary Stokes s
ystem with the Navier boundary condition\nby Professor Tai-Peng Tsai (
The University of British Columbia\, Vancouver\, Canada) as part of Fudan
International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstra
ct\nFor the non-stationary Stokes system\, it is well-known that one can i
mprove spatial regularity in the interior\, but not near the boundary if i
t is coupled with the no-slip boundary condition. In this talk I will show
that\, to the contrary and for the first time\, spatial regularity can be
improved near a flat boundary if it is coupled with the Navier boundary c
ondition with either infinite or finite slip length. The case with finite
slip length is more difficult than the case with infinite slip length. Thi
s is a joint work with Hui Chen and Su Liang\, and is dedicated to Vladim
ír Šverák on the occasion of his 65th birthday.\n\nPasscode for the vid
eolink:\nTfV^N@s8\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Ana Leonor Silvestre (Instituto Superior Técnico\, Univ
ersidade de Lisboa\, Portugal)
DTSTART:20240118T130000Z
DTEND:20240118T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/55
DESCRIPTION:Title: Far-field behavior of fluid flows and applications
\nby Professor Ana Leonor Silvestre (Instituto Superior Técnico\, Uni
versidade de Lisboa\, Portugal) as part of Fudan International Seminar on
Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nThis talk is devoted
to the analysis and applications of the spatial asymptotic profile of inco
mpressible viscous flows around a rigid body. The Stokes and Oseen fundame
ntal solutions play a crucial role in the mathematical analysis of the ext
erior problem and can be used to construct basis functions for a meshless
numerical method.\n\n#6qmm%&2\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Ludovic Rifford (Université Côte d’Azur & AIMS-Seneg
al)
DTSTART:20240201T130000Z
DTEND:20240201T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/56
DESCRIPTION:Title: On the minimizing Sard Conjecture in sub-Riemannia
n geometry\nby Professor Ludovic Rifford (Université Côte d’Azur &
AIMS-Senegal) as part of Fudan International Seminar on Analysis\, PDEs\,
and Fluid mechanics\n\n\nAbstract\nAfter recalling the notions of minimiz
ing geodesics and singular horizontal curves in sub-Riemannian geometry\,
we will discuss various versions of the so-called Sard conjecture and pres
ent several result dealing with the minimizing Sard Conjecture. The proof
of our main result will be sketched\, it relies on tools from non-smooth a
nalysis and geometric measure theory.\n\nPasscode for the videolink:\na1X6
e8?*\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Michael Winkler (Paderborn University\, Germany)
DTSTART:20240229T130000Z
DTEND:20240229T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/57
DESCRIPTION:Title: Can simple nutrient taxis interaction generate spa
tial structures?\nby Professor Michael Winkler (Paderborn University\,
Germany) as part of Fudan International Seminar on Analysis\, PDEs\, and
Fluid mechanics\n\n\nAbstract\nParabolic models for the collective behavio
r in populations of chemotactically migrating cells are considered. A focu
s will be on cases in which individuals are particularly primitive in the
sense that beyond a partially oriented movement toward increasing concentr
ations of a nutrient\, further activity can essentially be neglected. Rece
nt developments in the analysis of such nutrient taxis systems are to be d
escribed\, with a special emphasis set on mathematical challenges related
to the fundamental question how\n\nfar models of this type are capable of
adequately reflecting aspects of colorful dynamics known from experimental
observations.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Jan Burczak (University of Leipzig\, Germany)
DTSTART:20240411T130000Z
DTEND:20240411T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/58
DESCRIPTION:Title: Euler-driven scalar anomalous dissipation\nby
Professor Jan Burczak (University of Leipzig\, Germany) as part of Fudan I
nternational Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstrac
t\nI will present my recent result with L. Székelyhidi and B. Wu\, which
shows that any scalar advected by a typical weak solution of Euler equatio
n exhibits anomalous dissipation\, which is postulated as one of primary f
eatures of turbulence.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Maria Specovius (Universität Kassel\, Germany)
DTSTART:20240425T130000Z
DTEND:20240425T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/59
DESCRIPTION:Title: Some special aspects on the decomposition of vecto
r fields\nby Professor Maria Specovius (Universität Kassel\, Germany)
as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid mec
hanics\n\n\nAbstract\nThe decompositions of vector fields into a divergenc
e free part and a gradient field play a fundamental role in the theory of
the continuum mechanics\, in particular for the Navier- Stokes system. The
y are closely related to boundary value problems for the Laplace equation
and still objects of recent research\, lately in particular in unbounded d
omains and domains with nonsmooth boundaries. Of course\, it is not possi
ble to give a complete overview on more than thousand publications on this
subject in one lecture. The purpose of this lecture is to outline some of
the general principles\, in particular for domains with more or less expl
icitly given boundary singularities. In particular for so called model pro
blems it is astonishingly easy to combine well known results with duality
arguments to get a bunch of decomposition results.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Alexander Tyulenev (Steklov Mathematical Institute of Ru
ssian Academy of Sciences)
DTSTART:20240314T130000Z
DTEND:20240314T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/60
DESCRIPTION:Title: Traces of Sobolev spaces to irregular subsets and
Whitney problem\nby Professor Alexander Tyulenev (Steklov Mathematical
Institute of Russian Academy of Sciences) as part of Fudan International
Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nTrace theo
rems are the cornerstone of the theory of Sobolev spaces with many applica
tions. The trace problem was completely solved in classical works (O.V.Bes
ov et al.) for the case of manifolds\, i.e.\, the space of all traces is w
ell described\, the existence of an inverse bounded linear operator is pro
ved\, etc. Most of the classical results were subsequently transferred to
the case of Ahlfors-regular sets. At the same time\, the problem of descri
bing traces of Sobolev functions on arbitrary irregular compact sets remai
ns almost completely open. A similar problem for the case of functions wit
h classical smoothness was posed a long time ago by H. Whitney and has onl
y recently been solved in the works of Ch. Fefferman and his co-authors. H
owever\, the transition to the Sobolev case faces many difficulties that h
ave not yet been overcome. In this paper\, we will talk about recent progr
ess in this classical problem\, when traces are described for a fairly wid
e class of "thick sets" that can contain separate parts of different Hausd
orff dimensions. The results are valid not only for Euclidean spaces\, but
also for metric spaces with doubling measure.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Gianmarco Sperone (Pontifical Catholic University of C
hile)
DTSTART:20241024T130000Z
DTEND:20241024T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/61
DESCRIPTION:Title: On the planar Taylor--Couette system and related e
xterior problems\nby Professor Gianmarco Sperone (Pontifical Catholi
c University of Chile) as part of Fudan International Seminar on Analysis\
, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe consider the planar Taylor-
Couette system for the steady motion of a viscous incompressible fluid in
the region between two concentric disks\, the inner one being at rest and
the outer one rotating with constant angular speed. We study the uniquenes
s and multiplicity of solutions to the forced system in different classes.
For any angular velocity\, we prove that the classical Taylor-Couette flo
w is the unique smooth solution displaying rotational symmetry. Instead\,
we show that infinitely many solutions arise\, even for arbitrarily small
angular velocities\, in a larger class of incomplete solutions that we int
roduce. By prescribing the transversal flux\, the unique solvability of th
e Taylor-Couette system is recovered among rotationally invariant incomple
te solutions. Finally\, we study the behavior of these solutions as the ra
dius of the outer disk goes to infinity\, connecting our results with the
celebrated Stokes paradox. This is a joint work with Filippo Gazzola (Poli
tecnico di Milano) and Jiří Neustupa (Institute of Mathematics of the Cz
ech Academy of Sciences).\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Filippo Gazzola (Politecnico di Milano\, Italy)
DTSTART:20241107T130000Z
DTEND:20241107T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/62
DESCRIPTION:Title: New tools for detecting the epochs of irregularity
of Leray-Hopf solutions to some 3D Navier-Stokes equations\nby Profes
sor Filippo Gazzola (Politecnico di Milano\, Italy) as part of Fudan Inter
national Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nW
e study global Leray-Hopf solutions to Cauchy problems for the 3D Navier-S
tokes equations in a cube under Navier boundary conditions. With a suitabl
e reflection procedure\, these solutions become space-periodic over the wh
ole space R^3.\nSince the pioneering work by Jean Leray\, it is known that
solutions exist for any initial data with finite energy but it is not kno
wn whether their enstrophy may blow up in finite time in the so-called epo
chs of irregularity. Our simplified geometric and functional-analytic fram
ework enables us to determine explicit bounds both for the epochs of irreg
ularity and for the enstrophy. By using this information we bring strong e
vidence that the enstrophy blow-up may indeed occur in finite time due to
the energy equipartition among the Fourier components of the solution to a
finite-dimensional Galerkin approximation of the problem. This is a joint
work with Gianni Arioli and Alessio Falocchi.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Elia Brue (Department of Decision Sciences\, Bocconi Uni
versity)
DTSTART:20241121T130000Z
DTEND:20241121T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/63
DESCRIPTION:Title: Non-Uniqueness and Flexibility in Two-Dimensional
Euler Equations\nby Professor Elia Brue (Department of Decision Scienc
es\, Bocconi University) as part of Fudan International Seminar on Analysi
s\, PDEs\, and Fluid mechanics\n\n\nAbstract\nIn 1962\, Yudovich establish
ed the well-posedness of the two-dimensional incompressible Euler equation
s within the class of solutions with bounded vorticity. Since then\, a cen
tral unresolved problem has been the question of uniqueness within the bro
ader class of solutions with L^p-vorticities. Recent years have witnessed
significant progress in this investigation. In my talk\, I aim to provide
an overview of these developments and highlight recent results obtained th
anks to the convex integration method.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Sylvie Monniaux (Aix-Marseille Université (AMU))
DTSTART:20241205T130000Z
DTEND:20241205T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/64
DESCRIPTION:Title: The magnetohydrodynamical system in non smooth dom
ains\nby Professor Sylvie Monniaux (Aix-Marseille Université (AMU)) a
s part of Fudan International Seminar on Analysis\, PDEs\, and Fluid mecha
nics\n\n\nAbstract\nWe study the existence of solutions of the MHD system
(a coupling between a fluid and a magnetic field) in open subsets in 3 dim
ensions with Lipschitz regularity at the boundary. \nWe formulate the prob
lem with the help of differential forms which helps understanding the math
ematical problem and the boundary conditions. \nThe method employed to sho
w the existence of solutions is weighted maximal regularity for the linear
part of the problem and a fixed point theorem to treat the nonlinear part
.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Yurii Rykov (Keldysh Institute of Applied Mathematics\,
Russian Academy of Sciences)
DTSTART:20241212T130000Z
DTEND:20241212T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/65
DESCRIPTION:Title: On some non-standard fluid dynamics models and an
alternative approach to the conservation laws theory\nby Professor Yur
ii Rykov (Keldysh Institute of Applied Mathematics\, Russian Academy of Sc
iences) as part of Fudan International Seminar on Analysis\, PDEs\, and Fl
uid mechanics\n\n\nAbstract\nThe content of the talk is divided into two m
ain parts. The first part discusses two non-standard mathematical models o
f continuous medium flow\, which can be expressed as a quasi-linear system
of conservation laws. A key feature of these systems is that\, even under
smooth initial conditions\, their generalized solutions can have differen
t types of singularities in the general case. First\, we consider a one-di
mensional system of equations for compressible two-phase multi-component f
iltration. It will be shown how concepts from the theory of conservation l
aws can be used to study this system\, including\, for example\, the Riema
nn problem. However\, solutions to this problem will not exhibit the typic
al characteristics of the standard theory. Instead\, they will exhibit inf
inite propagation velocities and be always discontinuous. Second\, we will
consider dynamics in a two-dimensional isobaric medium\, which is a syste
m of equations of pressureless gas dynamics. It describes the phenomena of
matter concentration. This system of equations leads to the emergence of
strong singularities in the form of delta functions on manifolds of differ
ent dimensions. As a result\, specific Rankine-Hugoniot-type equations ari
se. During the evolution process\, singularities along curves in the plane
interact with each other\, leading to various configurations\, including
delta functions at a point. This process can be seen as the formation of a
n evolving hierarchy of singularities. In the second part of the talk\, we
will explore an alternative view on the nature of quasi-linear conservati
on laws systems based on a variational representation of generalized solut
ions. The form of this representation differs from traditional formulation
s used in the theory of second-order equations. Two such representations a
re discussed: 1) Based on the generalization of known results (starting wi
th the works of E. Hopf)\, which is a variational representation of soluti
ons for a single equation. 2) Based on the representation of generalized s
olutions as functionals in the trajectory space.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Ivan Kuznetsov (Novosibirsk State University)
DTSTART:20250220T130000Z
DTEND:20250220T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/66
DESCRIPTION:Title: Impulsive Navier-Stokes Equations\nby Professo
r Ivan Kuznetsov (Novosibirsk State University) as part of Fudan Internati
onal Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nThe p
resent report is devoted to impulsive Navier-Stokes equations. Moreover\,
under periodic boundary conditions\, such impulsive Euler equations can be
combined with inviscid limit of Navier-Stokes equations. Moreover\, inste
ad of the Dirac delta function $\\delta_{(t=0)}\,$ the Dirac swarm – li
near combination of the Dirac delta functions $\\sum\\limits_{i=1^N\\alpha
_i\\delta_{x=x_i}$– can be taken as a source term.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Emil Wiedemann (University Erlangen-Nürnberg\, Germany)
DTSTART:20250320T130000Z
DTEND:20250320T140000Z
DTSTAMP:20260404T111136Z
UID:Cafe_Analysis_and_Fluid/67
DESCRIPTION:Title: Non-Deterministic Solution Concepts in Fluid Dynam
ics\nby Professor Emil Wiedemann (University Erlangen-Nürnberg\, Germ
any) as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid
mechanics\n\n\nAbstract\nAs more and more ill-posedness results have been
shown for fluid PDEs (not only by convex integration!)\, the idea to solv
e the Cauchy problem by some unique weak or entropy solution has become qu
estionable. Instead\, non-deterministic solution concepts such as measure-
valued or statistical have sparked much recent research interest. They als
o seem to be more in line with well-known theories of turbulence\, which a
re typically statistical. I will give an overview of such generalised solu
tion concepts\, including their weak-strong stability\, their relation to
more conventional solutions\, and questions of existence.\n
LOCATION:https://stable.researchseminars.org/talk/Cafe_Analysis_and_Fluid/
67/
END:VEVENT
END:VCALENDAR