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BEGIN:VEVENT
SUMMARY:Weiren Zhao (NYU Abu Dhabi)
DTSTART:20200416T131500Z
DTEND:20200416T140500Z
DTSTAMP:20260404T111001Z
UID:IMS/1
DESCRIPTION:Title: Inviscid damping for a class of monotone shear flow\nby Weiren Zhao
(NYU Abu Dhabi) as part of PDE seminar via Zoom\n\n\nAbstract\nIn this ta
lk\, I am going to talk about the nonlinear inviscid damping for a class o
f monotone shear flows in the finite channel for initial perturbation in G
evrey class with compact support. The main idea of the proof is to use the
wave operator of a slightly modified Rayleigh operator in a well chosen c
oordinate system. This is a joint work with Nader Masmoudi.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Ros-Oton (Universität Zürich)
DTSTART:20200416T140500Z
DTEND:20200416T145500Z
DTSTAMP:20260404T111001Z
UID:IMS/2
DESCRIPTION:Title: Generic regularity of free boundaries for the obstacle problem\nby
Xavier Ros-Oton (Universität Zürich) as part of PDE seminar via Zoom\n\n
\nAbstract\nThe obstacle problem is the most classical and motivating exam
ple in the study of free boundary problems. A milestone in this context is
the classical work of Caffarelli (Acta Math. 1977)\, in which he establis
hed for the first time the regularity of free boundaries in the obstacle p
roblem\, outside a certain set of singular points. A long-standing open qu
estion in the field asks to establish generic regularity results in this s
etting (e.g. to prove that for ``almost every solution'' there are no sing
ular points). The goal of this talk is to present some new results in this
context\, proving in particular the generic regularity of free boundaries
for the obstacle problem in $\\R^3$. This is a joint work with A. Figalli
and J. Serra.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hui Yu (Columbia University)
DTSTART:20200416T150000Z
DTEND:20200416T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/3
DESCRIPTION:Title: Regularity of the singular set in the fully nonlinear obstacle problem<
/a>\nby Hui Yu (Columbia University) as part of PDE seminar via Zoom\n\n\n
Abstract\nObstacle problem is one of the well-studied free boundary proble
ms. When the operator is the Laplacian\, it is known that the free boundar
y consists of two parts: the regular part and the singular part. The regul
ar part is an analytic hypersurface\, and the singular part is covered by
C1-manifolds with various dimensions.\n\nWhile the tools for the study of
the regular part is robust enough that the theory has been generalized to
many other free boundary problems\, up to now all developments on the sing
ular part rely on monotonicity formulae. Such formulae are only expected f
or the Laplacian and linear operators with very regular coefficients. Cons
equently\, very little is known about the singular set when the operator i
s not the Laplacian.\n\nIn this talk we describe a new method to study the
singular set in the obstacle problem. This method does not depend on mono
tonicity formulae and works for fully nonlinear elliptic operators. The re
sult we get matches the best-known result for the case of Laplacian.\n\nTh
is is based on joint work with Ovidiu Savin from Columbia University.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elio Marconi (University of Basel)
DTSTART:20200423T130000Z
DTEND:20200423T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/4
DESCRIPTION:Title: Regularity estimates for the flow of BV autonomous divergence-free plan
ar vector fields\nby Elio Marconi (University of Basel) as part of PDE
seminar via Zoom\n\n\nAbstract\nWe consider the appropriate notion of flo
w $X$ associated to a bounded divergence-free vector field $b$ with bounde
d variation in the plane. We prove a Lusin-Lipschitz regularity result for
$X$ and we show that the Lipschitz constant grows at most linearly in tim
e. As a consequence we deduce that both geometric and analytical mixing ha
ve a lower bound of order $1/t$ as $t\\to \\infty$. This is a joint work w
ith Paolo Bonicatto.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Collot (Courant institute of mathematical Sciences)
DTSTART:20200423T140000Z
DTEND:20200423T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/5
DESCRIPTION:Title: On the derivation of the homogeneous kinetic wave equation\nby Char
les Collot (Courant institute of mathematical Sciences) as part of PDE sem
inar via Zoom\n\n\nAbstract\nThe kinetic wave equation arises in many phys
ical situations: the description of small random surface waves\, or out of
equilibria dynamics for large quantum systems for example. In this talk w
e are interested in its derivation as an effective equation from the nonli
near Schrodinger equation (NLS) for the microscopic description of a syste
m. More precisely\, we will consider (NLS) in a weakly nonlinear regime on
the torus in any dimension greater than two\, and for highly oscillatory
random Gaussian fields as initial data. A conjecture in statistical physic
s is that there exists a kinetic time scale on which\, statistically\, the
Fourier modes evolve according to the kinetic wave equation. We prove thi
s conjecture up to an arbitrarily small polynomial loss in a particular re
gime\, and obtain a more restricted time scale in other regimes. The main
difficulty\, that I will comment on\, is that one needs to identify the le
ading order statistically observable nonlinear effects. This means underst
anding correlation between Fourier modes\, and relating randomness with st
ability and local well-posedness. The key idea of the analysis is the use
of Feynman interaction diagrams to understand the solution as colliding li
near waves. We use this framework to construct an approximate solution as
a truncated series expansion\, and use in addition random matrices tools t
o obtain its nonlinear stability in Bourgain spaces. This is joint work wi
th P. Germain.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland)
DTSTART:20200423T150000Z
DTEND:20200423T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/6
DESCRIPTION:Title: The power spectrum of passive scalar turbulence in the Batchelor regime
\nby Jacob Bedrossian (University of Maryland) as part of PDE seminar
via Zoom\n\n\nAbstract\nIn 1959\, Batchelor predicted that passive scalars
advected in fluids at finite Reynolds number with small diffusivity κ sh
ould display a |k|−1 power spectrum over a small-scale inertial range in
a statistically stationary experiment. This prediction has been experimen
tally and numerically tested extensively in the physics and engineering li
terature and is a core prediction of passive scalar turbulence. Together w
ith Alex Blumenthal and Sam Punshon-Smith\, we have provided the first mat
hematically rigorous proof of this prediction for a scalar field evolving
by advection-diffusion in a fluid governed by the 2D Navier-Stokes equatio
ns and 3D hyperviscous Navier-Stokes equations in a periodic box subjected
to stochastic forcing at arbitrary Reynolds number. These results are pro
ved by studying the Lagrangian flow map using infinite dimensional extensi
ons of ideas from random dynamical systems. We prove that the Lagrangian f
low has a positive Lyapunov exponent (Lagrangian chaos) and show how this
can be upgraded to almost sure exponential (universal) mixing of passive s
calars at zero diffusivity and further to uniform-in-diffusivity mixing. T
his in turn is a sufficiently precise understanding of the low-to-high fre
quency cascade to deduce Batchelor's prediction.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Barker (École normale supérieure)
DTSTART:20200430T130000Z
DTEND:20200430T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/7
DESCRIPTION:Title: Quantitative estimates for the Navier-Stokes equations via spatial conc
entration\nby Tobias Barker (École normale supérieure) as part of PD
E seminar via Zoom\n\n\nAbstract\nIt remains open as to whether or not the
3D Navier-Stokes equations lose smoothness (`blow-up') in finite time. St
arting from Jean Leray\, many authors provided increasingly refined necess
ary conditions for a finite-time blow-up to occur. The majority of these b
low-up behaviours are formulated in terms of critical or subcritical quant
ities\, which are notions relating to the scaling symmetry of the Navier-S
tokes equations. Very recently\, Tao used a new quantitative approach to i
nfer that certain 'slightly supercritical' quantities for the Navier-Stoke
s equations must become unbounded near a potential blow-up.\n\n\nIn this t
alk I'll discuss a new strategy for proving quantitative bounds for the Na
vier-Stokes equations\, as well as applications to behaviours near a pote
ntial singularity . As a first application\, we prove a new potential blow
-up rate\, which is optimal for a certain class of potential non-zero back
ward discretely self-similar solutions. As a second application\, we quant
ify a conditional qualitative regularity result of Seregin (2012)\, which
says that if the critical L_{3} norm of the velocity field is bounded alo
ng a sequence of times tending to time $T$ then no blow-up occurs at time
$T$.\n\n\nThis talk is based upon joint work with Christophe Prange (CNRS
\, Université de Bordeaux).\n
LOCATION:https://stable.researchseminars.org/talk/IMS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (IAS\, Princeton)
DTSTART:20200430T140000Z
DTEND:20200430T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/8
DESCRIPTION:Title: The oriented Plateau problem and a question of Almgren\nby Camillo
De Lellis (IAS\, Princeton) as part of PDE seminar via Zoom\n\n\nAbstract\
nThe Plateau problem\, named by Henry Lebesgue after the Belgian physicist
Joseph Plateau\, consists in finding the surface of least area which span
s a given contour.\n\nIn order to tackle such question\, generations of ma
thematicians have investigated the very fundamental notions of ``surface''
\, ``boundary'' and ``area''\, proposing a variety of different theories.
\n\nIn this talk I will give a brief and intuitive exposition of an approa
ch to these concepts introduced by Federer and Fleming in the 60es after
the pioneering work of De Giorgi in the 50es. I will then discuss an open
question relating the shapes of the contour and that of the minimizer\, po
sed by Almgren in the early eighties and recently solved in a joint work w
ith Guido de Philippis\, Jonas Hirsch and Annalisa Massaccesi.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Deng (University of Southern California)
DTSTART:20200430T150000Z
DTEND:20200430T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/9
DESCRIPTION:Title: Derivation of the wave kinetic equation\nby Yu Deng (University of
Southern California) as part of PDE seminar via Zoom\n\n\nAbstract\nThe wa
ve turbulence theory describes the nonequilibrium statistical mechanics fo
r a large class of nonlinear dispersive systems. A major goal of this theo
ry is to derive the wave kinetic equation\, which predicts the behavior of
macroscopic limits of ensemble averages for microscopic interacting syste
ms. Usually this limit happens at a particular "kinetic time scale" in the
"weak-nonlinearity" limit where the number of interacting modes goes to i
nfinity while the nonlinearity strength goes to zero. For nonlinear Schrod
inger equations such limits have been derived on a formal level and studie
d extensively since the 1920s\, but a rigorous proof remains open.\n\n\nIn
this work\, joint with Zaher Hani\, we provide the first rigorous derivat
ion of wave kinetic equation\, which reaches the kinetic time scale up to
an arbitrary small power\, in a particular scaling regime for the number o
f modes and the strength of nonlinearity. We rely on a robust method\, whi
ch can be extended to other semilinear models\, and possibly also to quasi
linear models (such as water waves).\n
LOCATION:https://stable.researchseminars.org/talk/IMS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Raphael (University of Cambridge)
DTSTART:20200507T130000Z
DTEND:20200507T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/10
DESCRIPTION:Title: On blow up for the defocusing NLS and three dimensional viscous compre
ssible fluids\nby Pierre Raphael (University of Cambridge) as part of
PDE seminar via Zoom\n\n\nAbstract\nGlobal existence and scattering for th
e defocusing nonlinear Schrodinger equation is a celebrated result by Gini
bre-Velo in the early 80’s in the strictly energy sub critical case\, an
d Bourgain in 94 in the energy critical case. In the energy super critical
setting\, the defocusing energy is conserved and controls the energy norm
\, but this is too weak to conclude to global existence which yet had been
conjectured by many and confirmed by numerical computations. This is a ca
nonical super critical problem which typically arises similarily in fluid
mechanics\, and there global existence is either completely open or a di
rect consequence of the existence of additional conservation laws. In this
talk based on recent joint works with Merle (IHES)\, Rodnianski (Princeto
n) and Szeftel (Paris Sorbonne)\, I will describe the construction of news
mooth and finite energy highly oscillatory blow up solutions for the defo
cusing NLS in suitable energy super critical regimes\, and explain how the
se new bubbles are connected to the also new description of implosion mech
anisms for viscous three dimensional compressible fluids.\n\nHere is the p
oster of this talk: https://www.dropbox.com/s/3pgqawpbjh20g6m/5th%20PDE%20
Seminar.pdf?dl=0\n\nPlease visit our website to get more information: \nht
tps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guido De Philippis (Courant institute of mathematical Sciences)
DTSTART:20200507T140000Z
DTEND:20200507T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/11
DESCRIPTION:Title: Regularity of the free boundary for the two-phase Bernoulli problem\nby Guido De Philippis (Courant institute of mathematical Sciences) as p
art of PDE seminar via Zoom\n\n\nAbstract\nI will illustrate a recent res
ult obtained in collaboration with L. Spolaor and B. Velichkov concernin
g the regularity of the free boundaries in the two phase Bernoulli problem
s. The new main point is the analysis of the free boundary close to branch
points\, where we show that it is given by the union of two C^1 graphs. T
his complete the analysis started by Alt Caffarelli Friedman in the 80’s
\n\nHere is the poster of this talk: https://www.dropbox.com/s/3pgqawpbjh2
0g6m/5th%20PDE%20Seminar.pdf?dl=0\n\nPlease visit our website to get more
information: \nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-semin
ar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:In-Jee Jeong (Korea Institute for Advanced Study (KIAS))
DTSTART:20200514T130000Z
DTEND:20200514T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/12
DESCRIPTION:Title: Well-posedness for the axisymmetric Euler equations\nby In-Jee Jeo
ng (Korea Institute for Advanced Study (KIAS)) as part of PDE seminar via
Zoom\n\n\nAbstract\nThe incompressible Euler equations describe the motion
of inviscid and volume-preserving fluids. The equations respect rotationa
l symmetries\, and if one considers initial data which is invariant under
all rotations fixing an axis\, this property holds for the solution as wel
l. The resulting axisymmetric Euler equations look rather simple\, but as
we shall see in this talk\, even the basic question of well-posedness turn
s out to be very delicate.\n\nHere is the poster of this talk: www.dropbox
.com/s/htly5kmdcl2dfw2/PDE%20Seminar%206th.pdf?dl=0\n\nPlease visit our we
bsite to get more information: \nhttps://nguyenquochung1241.wixsite.com/qh
ung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Drivas (Princeton University)
DTSTART:20200514T150000Z
DTEND:20200514T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/13
DESCRIPTION:Title: Quasisymmetric plasma equilibria with small forcing\nby Theodore D
rivas (Princeton University) as part of PDE seminar via Zoom\n\n\nAbstract
\nQuasisymmetry is a structural property of a magnetic field which ensure
s that charge particles remain well confined within the guiding centre app
roximation of their motion. Identifying plasma equilibria enjoying this pr
operty is a key part of ongoing attempts to achieve efficient plasma fusio
n. I will discuss the construction of toroidal equilibria which achieve qu
asisymmetry and are sustained by a small forcing.\n\nHere is the poster of
this talk: www.dropbox.com/s/htly5kmdcl2dfw2/PDE%20Seminar%206th.pdf?dl=0
\n\nPlease visit our website to get more information: \nhttps://nguyenquoc
hung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabelle Gallagher (École normale supérieure)
DTSTART:20200521T130000Z
DTEND:20200521T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/14
DESCRIPTION:Title: From Newton to Boltzmann\, fluctuations and large deviations\nby I
sabelle Gallagher (École normale supérieure) as part of PDE seminar via
Zoom\n\n\nAbstract\nI will report on a recent work\, joint with Th. Bodine
au\, L. Saint-Raymond and S. Simonella\, in which we develop a rigorous th
eory of macroscopic fluctuations for a hard sphere gas outside thermal equ
ilibrium\, in the Boltzmann-Grad limit : in particular we study deviations
from the Boltzmann equation (describing the asymptotic dynamics of the em
pirical density) and provide\, for short kinetic times\, both a central li
mit theorem and large deviation bounds.\n\nHere is the poster of this talk
: https://www.dropbox.com/s/807vg0v0nrmlp2d/PDE%20Seminar%207th.pdf?dl=0\n
Please visit our website to get more information: nguyenquochung1241.wixsi
te.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toan T. Nguyen (Penn State University)
DTSTART:20200528T130000Z
DTEND:20200528T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/15
DESCRIPTION:Title: Landau damping and Plasma echoes\nby Toan T. Nguyen (Penn State Un
iversity) as part of PDE seminar via Zoom\n\n\nAbstract\nThe talk presents
an elementary proof of the nonlinear Landau damping for analytic and Gevr
ey data that was first obtained by Mouhot and Villani and subsequently ext
ended by Bedrossian\, Masmoudi\, and Mouhot. The construction of an infini
te cascade of plasma echoes\, that do not belong to the analytic or Gevrey
classes\, but do\, nonetheless\, exhibit damping phenomena for large time
s\, will also be presented. This is a joint work with Emmanuel Grenier (EN
S Lyon) and Igor Rodnianski (Princeton).\n\nHere is the poster of this tal
k: https://www.dropbox.com/s/ris7y3bbubt6xhu/PDE%20Seminar%208th.pdf?dl=0\
nPlease visit our website to get more information: nguyenquochung1241.wixs
ite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Emmanuel Jabin (University of Maryland)
DTSTART:20200528T140000Z
DTEND:20200528T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/16
DESCRIPTION:Title: Large stochastic systems of interacting particles\nby Pierre-Emman
uel Jabin (University of Maryland) as part of PDE seminar via Zoom\n\n\nAb
stract\nI will present some recent results\, obtained with D. Bresch and Z
. Wang\, on large stochastic many-particle or multi-agent systems. Because
such systems are conceptually simple but exhibit a wide range of emerging
macroscopic behaviors\, they are now employed in a large variety of appli
cations from Physics (plasmas\, galaxy formation...) to the Biosciences\,
Economy\, Social Sciences...\n\nThe number of agents or particles is typic
ally quite large\, with 10^{20}-10^{25} particles in many Physics settings
for example and just as many equations. Analytical or numerical studies o
f such systems are potentially very complex leading to the key question a
s to whether it is possible to reduce this complexity\, notably thanks to
the notion of propagation of chaos (agents remaining almost uncorrelated).
\n\nTo derive this propagation of chaos\, we have introduced a novel analy
tical method\, which led to the resolution of two long-standing conjecture
s:\n\n1) The quantitative derivation of the 2-dimensional incompressible N
avier-Stokes system from the point vortices dynamics\;\n\n2) The derivatio
n of the mean-field limit for attractive singular interactions such as in
the Keller-Segel model for chemotaxis and some Coulomb gases.\n\nHere is t
he poster of this talk: https://www.dropbox.com/s/ris7y3bbubt6xhu/PDE%20Se
minar%208th.pdf?dl=0\nPlease visit our website to get more information: ng
uyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Ionescu (Princeton University)
DTSTART:20200514T140000Z
DTEND:20200514T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/17
DESCRIPTION:Title: Nonlinear stability of vortices and shear flows\nby Alexandru Ione
scu (Princeton University) as part of PDE seminar via Zoom\n\n\nAbstract\n
I will talk about some recent work on the nonlinear asymptotic\n\nstabilit
y of point vortices and monotonic shear flows among solutions of the 2D Eu
ler equations. This is joint work with Hao Jia.\n\nHere is the poster of t
his talk: www.dropbox.com/s/htly5kmdcl2dfw2/PDE%20Seminar%206th.pdf?dl=0\n
\nPlease visit our website to get more information: \nhttps://nguyenquochu
ng1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Colombo (Ecole polytechnique fédérale de Lausanne)
DTSTART:20200521T140000Z
DTEND:20200521T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/18
DESCRIPTION:Title: Weak solutions of the Navier-Stokes equations may be smooth for a.e. t
ime\nby Maria Colombo (Ecole polytechnique fédérale de Lausanne) as
part of PDE seminar via Zoom\n\n\nAbstract\nRecently\, Buckmaster and Vico
l proved non-uniqueness of weak solutions to the Navier-Stokes equations w
hich have bounded kinetic energy and integrable vorticity. We review the c
urrent developments of the topic\, based on the so called convex integrati
on construction\, and discuss in particular the existence of such solution
s\, which in addition are regular outside a set of times of dimension less
than 1.\n\nHere is the poster of this talk: https://www.dropbox.com/s/807
vg0v0nrmlp2d/PDE%20Seminar%207th.pdf?dl=0\nPlease visit our website to get
more information: nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-v
ia-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Didier Bresch (Université Savoie Mont-Blanc)
DTSTART:20200507T150000Z
DTEND:20200507T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/19
DESCRIPTION:Title: On the stationary compressible Navier-Stokes equations\nby Didier
Bresch (Université Savoie Mont-Blanc) as part of PDE seminar via Zoom\n\n
\nAbstract\nIn this talk\, I remind known results regarding weak solutions
for the isotropic stationary compressible Navier-Stokes equations with co
nstant shear and bulk viscosities. Then I will present how to extend the
results to more general stress tensors including anisotropy and non-local
terms. This seminar is based on joint works with Cosmin Burtea (IMJ Paris
7\, France).\n\nHere is the poster of this talk: https://www.dropbox.com/s
/3pgqawpbjh20g6m/5th%20PDE%20Seminar.pdf?dl=0\n\nPlease visit our website
to get more information: \nhttps://nguyenquochung1241.wixsite.com/qhung/po
st/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Fischer (Institute of Science and Technology Austria (IST A
ustria))
DTSTART:20200521T150000Z
DTEND:20200521T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/20
DESCRIPTION:Title: Weak-strong uniqueness principles for interface evolution problems in
fluid mechanics and geometry\nby Julian Fischer (Institute of Science
and Technology Austria (IST Austria)) as part of PDE seminar via Zoom\n\n\
nAbstract\nIn evolution equations for interfaces\, topological changes and
geometric singularities occur naturally\, one basic example being the pin
choff of liquid droplets. As a consequence\, classical solution concepts f
or such PDEs are naturally limited to short-time existence results or part
icular initial configurations like perturbations of a steady state. At the
same time\, the transition from strong to weak solution concepts for PDEs
is prone to incurring unphysical non-uniqueness of solutions. In the abse
nce of a comparison principle\, the relation between weak solution concept
s and strong solution concepts for interface evolution problems has remain
ed a mostly open question. We establish weak-strong uniqueness principles
for two important interface evolution problems\, namely for planar multiph
ase mean curvature flow and for the evolution of the free boundary between
two viscous fluids: As long as a classical solution to these evolution pr
oblems exists\, it is also the unique BV solution respectively varifold so
lution. In the case of multiphase mean curvature flow\, our construction l
eads to a gradient-flow analogue of the notion of calibrations.\n\nBased o
n joint works with Sebastian Hensel\, Tim Laux\, and Thilo Simon.\n\nHere
is the poster of this talk: https://www.dropbox.com/s/807vg0v0nrmlp2d/PDE%
20Seminar%207th.pdf?dl=0\nPlease visit our website to get more information
: nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Yizhao Hou (California Institute of Technology)
DTSTART:20200528T150000Z
DTEND:20200528T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/21
DESCRIPTION:Title: Recent Progress on Singularity Formation of 3D Euler Equations and Rel
ated Models\nby Thomas Yizhao Hou (California Institute of Technology)
as part of PDE seminar via Zoom\n\n\nAbstract\nWhether the 3D incompressi
ble Euler equations can develop a singularity in finite time from smooth i
nitial data is one of the most challenging problems in mathematical fluid
dynamics. We first review the numerical evidence of finite time singularit
y for 3D axisymmetric Euler equations by Luo and Hou. The singularity is a
ring like singularity that occurs at a stagnation point in the symmetry p
lane located at the boundary of the cylinder. We then present a novel meth
od of analysis and prove that the 1D HL model develops finite time self-si
milar singularity. We also apply this method of analysis to prove finite t
ime self-similar blowup of the original De Gregorio model for some smooth
initial data on the real line with compact support. Self-similar blowup r
esults for the generalized De Gregorio model for the entire range of param
eter on the real line or on a circle have been obtained for Holder continu
ous initial data with compact support. Finally\, we report our recent prog
ress in analyzing the finite time singularity of the axisymmetric 3D Euler
equations with initial data considered by Luo and Hou.\n\nHere is the pos
ter of this talk: https://www.dropbox.com/s/ris7y3bbubt6xhu/PDE%20Seminar%
208th.pdf?dl=0\nPlease visit our website to get more information: nguyenqu
ochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Coti Zelati (Imperial College London)
DTSTART:20200604T130000Z
DTEND:20200604T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/22
DESCRIPTION:Title: Inviscid damping and enhanced dissipation in 2d fluids\nby Michele
Coti Zelati (Imperial College London) as part of PDE seminar via Zoom\n\n
\nAbstract\nWe review some recent results on the asymptotic stability of s
tationary solutions to the two-dimensional Euler and Navier-Stokes equatio
ns of incompressible flows. In many cases\, sharp decay rates for the line
arized problem imply some sort of nonlinear asymptotic stability\, both in
the Euler equations (through the so-called inviscid damping) and the Nav
ier-Stokes equations (undergoing enhanced dissipation). However\, we will
see that in the case of the 2D square periodic domain\, the so-called Kolm
ogorov flow exhibits much more complex behavior: in particular\, linear as
ymptotic stability holds\, while nonlinear asymptotic stability is not tru
e even for analytic perturbations.\n\nHere is the poster of this talk: \nh
ttps://www.dropbox.com/s/3ixoc26oxs2tblj/9th%20PDE%20Seminar.pdf?dl=0\n\nP
lease visit our website to get more information: \n\nhttps://nguyenquochun
g1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Alazard (École Normale Supérieure de Paris-Saclay)
DTSTART:20200604T140000Z
DTEND:20200604T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/23
DESCRIPTION:Title: Entropies of free surface flows in fluid dynamics\nby Thomas Alaza
rd (École Normale Supérieure de Paris-Saclay) as part of PDE seminar via
Zoom\n\n\nAbstract\nI will discuss recent works with Didier Bresch\, Nico
las Meunier and Didier Smets about the dynamics of a free surface transpor
ted by an incompressible flow obeying Darcy’s law. I will consider the H
ele-Shaw and Mullins-Sekerka equations\, as well as the thin-film and Bous
sinesq equations. For these equations\, I will present monotonicity proper
ties of different natures : maximum principles\, Lyapunov functionals and
entropies. The analysis is based on exact identities which in turn allow t
o study the Cauchy problem for classical solutions in any subcritical Sobo
lev spaces.\n\nHere is the poster of this talk: \nhttps://www.dropbox.com/
s/3ixoc26oxs2tblj/9th%20PDE%20Seminar.pdf?dl=0\n\nPlease visit our website
to get more information: \n\nhttps://nguyenquochung1241.wixsite.com/qhung
/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phan Thanh Nam (LMU Munich)
DTSTART:20200604T150000Z
DTEND:20200604T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/24
DESCRIPTION:Title: Derivation of the Bose-Einstein condensation for trapped bosons\nb
y Phan Thanh Nam (LMU Munich) as part of PDE seminar via Zoom\n\nAbstract:
TBA\n\nHere is the poster of this talk: \nhttps://www.dropbox.com/s/3ixoc
26oxs2tblj/9th%20PDE%20Seminar.pdf?dl=0\n\nPlease visit our website to get
more information: \n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/p
de-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhifei Zhang (Peking university)
DTSTART:20200611T130000Z
DTEND:20200611T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/25
DESCRIPTION:Title: Transition threshold for the 3D Couette flow in a finite channel\n
by Zhifei Zhang (Peking university) as part of PDE seminar via Zoom\n\n\nA
bstract\nThe plane Couette flow is linearly stable for any Reynolds number
. However\, it could become nonlinearly unstable and transition to turbule
nce for small but finite perturbations at high Reynolds number. This is so
-called Sommerfeld paradox. \nOne resolution of this paradox is to study t
he transition threshold problem\, which is concerned with how much disturb
ance will lead to the instability of the flow and the dependence of distur
bance on the Reynolds number. In a joint work with Qi Chen and Dongyi Wei\
, we showed that if the initial velocity $v_0$ satisfies $\\|v_0-(y\,0\,0)
\\|_{H^2}\\le c_0{Re}^{-1}$ for some $c_0>0$ independent of $Re$\, then th
e solution of the 3D Navier-Stokes equations is global in time and does no
t transition away from the Couette flow in the $L^\\infty$ sense\, and rap
idly converges to a streak solution for $t\\gtrsim Re^{1/3}$ due to the mi
xing-enhanced dissipation effect. This result confirms the transition thre
shold conjecture proposed by Trefethen et al.(Science\, 261(1993)\, 578-58
4) for the 3D Couette flow in a finite channel with non-slip boundary cond
ition.\n\nHere is the poster of this talk:https://www.dropbox.com/s/gxyo8w
hzqnvco3h/The%2010th%20PDE%20Seminar.png?dl=0\n\nPlease visit our website
to get more information: nguyenquochung1241.wixsite.com/qhung/post/pde-sem
inar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clément Mouhot (University of Cambridge)
DTSTART:20200611T140000Z
DTEND:20200611T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/26
DESCRIPTION:Title: Unified approach to fluid approximation of linear kinetic equations wi
th heavy tails\nby Clément Mouhot (University of Cambridge) as part o
f PDE seminar via Zoom\n\n\nAbstract\nThe rigorous fluid approximation of
linear kinetic equations was first obtained in the late 70s when the equil
ibrium distribution decays faster than polynomials. In this case the limit
is a diffusion equation. In the case of heavy tail equilibrium distributi
on (with infinite variance)\, the first rigorous derivation was obtained i
n 2011 in my joint paper with Mellet and Mischler\, in the case of scatter
ing operators. The limit shows then anomalous diffusion\; it is governed b
y a fractional diffusion equation. Lebeau and Puel proved last year the fi
rst similar result for Fokker-Planck operator\, in dimension 1 and assumin
g that the equilibrium distribution has finite mass. Fournier and Tardif g
ave an alternative probabilistic proof\, more general (covering any dimens
ion and infinite-mass equilibrium distribution) but non-constructive. We p
resent a unified quantitative PDE approach that obtains constructively the
limit for Fokker-Planck operators in dimensions greater than 2\, but also
recovers and unifies the previous works. This is a joint work with Emeric
Bouin (Université Paris-Dauphine).\n\nHere is the poster of this talk: h
ttps://www.dropbox.com/s/gxyo8whzqnvco3h/The%2010th%20PDE%20Seminar.png?dl
=0\n\nPlease visit our website to get more information: nguyenquochung1241
.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART:20200611T150000Z
DTEND:20200611T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/27
DESCRIPTION:Title: Regularity estimates for the Boltzmann equation without cutoff\nby
Luis Silvestre (University of Chicago) as part of PDE seminar via Zoom\n\
n\nAbstract\nWe study the regularization effect of the inhomogeneous Boltz
mann equation without cutoff. We obtain a priori estimates for all derivat
ives of the solution depending only on bounds of the hydrodynamic quantiti
es: mass density\, energy density and entropy density. As a consequence\,
a classical solution to the equation may fail to exists after certain time
T only if at least one of these hydrodynamic quantities blows up. Our ana
lysis applies to the case of moderately soft and hard potentials. We use m
ethods that originated in the study of nonlocal elliptic equations: a weak
Harnack inequality in the style of De Giorgi\, and a Schauder-type estima
te.\n\nHere is the poster of this talk: www.dropbox.com/s/gxyo8whzqnvco3h/
The%2010th%20PDE%20Seminar.png?dl=0\n\nPlease visit our website to get mor
e information: nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-z
oom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Engelstein (University of Minnesota)
DTSTART:20200618T140000Z
DTEND:20200618T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/28
DESCRIPTION:Title: An Epiperimetric Approach to Isolated Singularities\nby Max Engels
tein (University of Minnesota) as part of PDE seminar via Zoom\n\n\nAbstra
ct\nThe presence of singular points (i.e. points around which the object i
n question does not look flat at any scale) is inevitable in most minimiza
tion problems. One fundamental question is whether minimizers have a uniqu
e tangent object at singular points i.e.\, is the minimizer increasingly w
ell approximated by some other minimizing object as we “zoom in” at a
singular point. This question has been investigated with varying degrees o
f success in the settings of minimal surfaces\, harmonic maps and obstacle
problems amongst others.\n\nIn this talk\, we will present an uniqueness
of blowups result for minimizers of the Alt-Caffarelli functional. In part
icular\, we prove that the tangent object is unique at isolated singular p
oints in the free boundary. Our main tool is a new approach to proving (lo
g-)epiperimetric inequalities at isolated singularities. This epiperimetri
c inequality differs from previous ones in that it holds without any addit
ional assumptions on the symmetries of the tangent object.\n\nIf we have t
ime\, we will also discuss how this method allows us to recover some uniqu
eness of blow-ups results in the minimal surfaces setting\, particularly t
hose of Allard-Almgren (’81) and Leon Simon (’83). This is joint work
with Luca Spolaor (UCSD) and Bozhidar Velichkov (U. Napoli).\n\nhttps://ng
uyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Pausader (Brown University)
DTSTART:20200618T150000Z
DTEND:20200618T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/29
DESCRIPTION:Title: Stability of the Minkowski space for the Einstein-Klein-Gordon system<
/a>\nby Benoit Pausader (Brown University) as part of PDE seminar via Zoom
\n\n\nAbstract\nWe consider the Einstein-Klein-Gordon system which models
the evolution of a Lorentzian metric associated to one of the simplest mat
ter models (the Klein-Gordon equation) and we consider small perturbations
which decay slowly (more slowly than 1/r)\, and show that the spacetime c
onstructed are global and converge back to Minkowski through some modified
scattering and describe their properties. This is a joint work with A. Io
nescu.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-vi
a-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Gilles Lemarié-Rieusset (Laboratoire de Mathématiques et
Modélisation d'Évry)
DTSTART:20200625T130000Z
DTEND:20200625T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/30
DESCRIPTION:Title: On weak solutions of the Navier-Stokes equations with infinite energy<
/a>\nby Pierre Gilles Lemarié-Rieusset (Laboratoire de Mathématiques et
Modélisation d'Évry) as part of PDE seminar via Zoom\n\n\nAbstract\nOne
year ago\, Bradshaw and Tsai and\, quite independently\, Fernandez and Lem
arié-Rieusset announced results of global existence of weak solutions for
the incompressible Navier-Stokes equations that had poor decay at infinit
y. In my talk\, I will review some issues on the regularity of such soluti
ons (joint work with Pedro Fernandez).\n\nhttps://nguyenquochung1241.wixsi
te.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert M. Strain (University of Pennsylvania)
DTSTART:20200625T140000Z
DTEND:20200625T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/31
DESCRIPTION:Title: Global mild solutions of the Landau and non-cutoff Boltzmann equation<
/a>\nby Robert M. Strain (University of Pennsylvania) as part of PDE semin
ar via Zoom\n\n\nAbstract\nIn this talk we explain a recent proof of the e
xistence of small-amplitude global-in-time unique mild solutions to both t
he Landau equation including the Coulomb potential and the Boltzmann equat
ion without angular cutoff. Since the well-known works (Guo\, 2002) and
(Gressman-Strain-2011\, AMUXY-2012) on the construction of classical solut
ions in smooth Sobolev spaces which in particular are regular in the spati
al variables\, it has still remained an open problem to obtain global solu
tions in an $L^\\infty_{x\,v}$ framework\, similar to that in (Guo-2010)\,
for the Boltzmann equation with cutoff in general bounded domains. \n\n\
n\n\nOne main difficulty arises from the interaction between the transport
operator and the velocity-diffusion-type collision operator in the non-cu
toff Boltzmann and Landau equations\; another major difficulty is the pote
ntial formation of singularities for solutions to the boundary value probl
em. \n\n\n\n\nIn this work we introduce a new function space with low regu
larity in the spatial variable to treat the problem in cases when the spat
ial domain is either a torus\, or a finite channel with boundary. For the
latter case\, either the inflow boundary condition or the specular reflect
ion boundary condition is considered. An important property of the functio
n space is that the $L^\\infty_T L^2_v$ norm\, in velocity and time\, of t
he distribution function is in the Wiener algebra $A(\\Omega)$ in the spa
tial variables. \n\n\n\n\nBesides the construction of global solutions in
these function spaces\, we additionally study the large-time behavior of
solutions for both hard and soft potentials\, and we further justify the p
roperty of propagation of regularity of solutions in the spatial variables
. To the best of our knowledge these results may be the first ones to pro
vide an elementary understanding of the existence theories for the Landau
or non-cutoff Boltzmann equations in the situation where the spatial domai
n has a physical boundary. \n\n\n\n\nThis is a joint work with Renjun Dua
n (The Chinese University of Hong Kong)\, Shuangqian Liu (Jinan University
) and Shota Sakamoto (Tohoku University).\n\nhttps://nguyenquochung1241.wi
xsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung-Jin Oh (University of California Berkeley)
DTSTART:20200625T150000Z
DTEND:20200625T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/32
DESCRIPTION:Title: On the Cauchy problem for the Hall magnetohydrodynamics\nby Sung-J
in Oh (University of California Berkeley) as part of PDE seminar via Zoom\
n\n\nAbstract\nIn this talk\, I will describe a recent series of work with
I.-J. Jeong on the Hall MHD equation without resistivity. This PDE\, firs
t investigated by the applied mathematician M. J. Lighthill\, is a one-flu
id description of magnetized plasmas with a quadratic second-order correct
ion term (Hall current term)\, which takes into account the motion of elec
trons relative to positive ions. Curiously\, we demonstrate the ill(!)pose
dness of the Cauchy problem near the trivial solution\, despite the appare
nt linear stability and conservation of energy. On the other hand\, we ide
ntify several regimes in which the Cauchy problem is well-posed\, which no
t only includes the original setting that M. J. Lighthill investigated (na
mely\, for initial data close to a uniform magnetic field) but also possib
ly large perturbations thereof. Central to our proofs is the viewpoint tha
t the Hall current term imparts the magnetic field equation with a quasili
near dispersive character. With such a viewpoint\, the key ill- and well-p
osedness mechanisms can be understood in terms of the properties of the bi
characteristic flow associated with the appropriate principal symbol.\n\nh
ttps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Pusateri (University of Toronto)
DTSTART:20200618T130000Z
DTEND:20200618T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/33
DESCRIPTION:Title: Multilinear Harmonic analysis for nonlinear PDEs with potentials\n
by Fabio Pusateri (University of Toronto) as part of PDE seminar via Zoom\
n\n\nAbstract\nMotivated by questions on the stability of topological soli
tons\, we study some nonlinear dispersive PDEs with large potentials. Our
approach is based on the distorted Fourier transform and multilinear harmo
nic analysis in this setting. We will present results in both 1 and 3 dime
nsions from a series of joint works with P. Germain\, G. Chen and A. Soffe
r.\n\nPlease visit our website to get more information: nguyenquochung1241
.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massimiliano Berti (SISSA)
DTSTART:20200702T130000Z
DTEND:20200702T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/34
DESCRIPTION:Title: Long time dynamics of water waves\nby Massimiliano Berti (SISSA) a
s part of PDE seminar via Zoom\n\n\nAbstract\nI will present some long tim
e existence results of the solutions of the water waves equations for bidi
mensional perfect fluids under space periodic boundary conditions as well
as the existence of small amplitude time quasi-periodic solutions.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Burq (Institut de Mathématiques d'Orsay)
DTSTART:20200702T140000Z
DTEND:20200702T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/35
DESCRIPTION:Title: Control for wave equations: revisiting the geometric control condition
30 years later\nby Nicolas Burq (Institut de Mathématiques d'Orsay)
as part of PDE seminar via Zoom\n\n\nAbstract\nFollowing the pioneering wo
rk by Bardos-Lebeau and Rauch\, the property of controllability for the wa
ve equation has been intensively studied\, mainly in a smooth framework (s
mooth metric and smooth domain). In this lecture\, and I shall present so
me new results on observability/control for the wave equation with rough c
oefficients. This question leads to some interesting ODE questions for vec
tor fields with only continuous coefficients.\n\n\nThis is joint work B. D
ehman (Université Tunis El Manar) and J. Le Rousseau (Université Paris
13).\n
LOCATION:https://stable.researchseminars.org/talk/IMS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huy Nguyen (Brown University)
DTSTART:20200702T150000Z
DTEND:20200702T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/36
DESCRIPTION:Title: Proof of modulational instability of Stokes waves in deep water\nb
y Huy Nguyen (Brown University) as part of PDE seminar via Zoom\n\n\nAbstr
act\nIt is proven that small-amplitude steady periodic water waves with in
finite depth are unstable with respect to long-wave perturbations. This mo
dulational instability was first observed more than half a century ago by
Benjamin and Feir.\n\nIt has never been proven rigorously except in the ca
se of finite depth. We provide a completely different and self-contained a
pproach to prove the spectral modulational instability for water waves in
both the finite and infinite depth cases. Our linearization retains the ph
ysical variables and is compatible with energy estimates for the nonlinea
r problem.\n\n\nThis is joint work with Walter Strauss (Brown University).
\n
LOCATION:https://stable.researchseminars.org/talk/IMS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Tolsa (Autonomous University of Barcelona)
DTSTART:20200709T130000Z
DTEND:20200709T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/37
DESCRIPTION:Title: Unique continuation at the boundary for harmonic functions\nby Xav
ier Tolsa (Autonomous University of Barcelona) as part of PDE seminar via
Zoom\n\n\nAbstract\nIn a work from 1991 Fang-Hua Lin asked the following q
uestion. Let $\\Omega\\subset\\mathbb R^n$ be a Lipschitz domain. Let $u$
be a function harmonic in $\\Omega$ and continuous in $\\overline \\Omega$
which vanishes et $\\Sigma \\subset \\partial\\Omega$ and moreover assume
that the normal derivative $\\partial_\\nu u$ vanishes in a subset of $\\
Sigma$ with positive surface measure. Is it true that then $u$ is identica
lly zero? \n\nUp to now\, the answer was known to be positive for $C^1$-Di
ni domains\, by results of Adolfsson-Escauriaza (1997) and Kukavica-Nystro
m (1998). In this talk I will explain a recent work where I show that the
result also holds for Lipschitz domains with small Lipschitz constant\, an
d thus in particular for general $C^1$ domains.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan-Vasile Matioc (University of Regensburg)
DTSTART:20200709T140000Z
DTEND:20200709T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/38
DESCRIPTION:Title: The Muskat problem in subcritical Lp-Sobolev spaces\nby Bogdan-Vas
ile Matioc (University of Regensburg) as part of PDE seminar via Zoom\n\n\
nAbstract\nThe Muskat problem is a classical mathematical model which desc
ribes the motion of two immiscible and incompressible Newtonian fluids in
an homogeneous porous medium. The mathematical model posed in the entire p
lane can be formulated as an evolution equation for the function that para
metrizes the free boundary between the fluids. When neglecting surface ten
sion effects\, the evolution equation is fully nonlinear and nonlocal and
it involves singular integral operators defined by kernels that depend non
linearly on the unknown. We prove that the evolution problem is of parabol
ic type in the regime where the Rayleigh-Taylor condition is satisfied. Ba
sed upon this feature we establish the well posedness of the Muskat proble
m in all subcritical Lp-Sobolev spaces together with a parabolic smoothing
property. This is a joint work with Helmut Abels.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Isett (University of Texas at Austin)
DTSTART:20200709T150000Z
DTEND:20200709T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/39
DESCRIPTION:Title: A Proof of Onsager’s Conjecture for the Incompressible Euler Equatio
ns\nby Philip Isett (University of Texas at Austin) as part of PDE sem
inar via Zoom\n\n\nAbstract\nIn an effort to explain how anomalous dissipa
tion of energy occurs in hydrodynamic turbulence\, Onsager conjectured in
1949 that weak solutions to the incompressible Euler equations may fail to
exhibit conservation of energy if their spatial regularity is below 1/3-H
ölder. I will discuss a proof of this conjecture that shows that there a
re nonzero\, (1/3-\\epsilon)-Hölder Euler flows in 3D that have compact s
upport in time. The construction is based on a method known as "convex in
tegration\," which has its origins in the work of Nash on isometric embedd
ings with low codimension and low regularity. A version of this method wa
s first developed for the incompressible Euler equations by De Lellis and
Székelyhidi to build Hölder-continuous Euler flows that fail to conserve
energy\, and was later improved by Isett and by Buckmaster-De Lellis-Szé
kelyhidi to obtain further partial results towards Onsager's conjecture.
The proof of the full conjecture combines convex integration using the “
Mikado flows” introduced by Daneri-Székelyhidi with a new “gluing app
roximation” technique.The latter technique exploits a special structure
in the linearization of the incompressible Euler equations.\n\nPlease visi
t the following link: https://nguyenquochung1241.wixsite.com/qhung/post/pd
e-seminar-via-zoom to get more information.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omar Lazar (University of Seville)
DTSTART:20200716T130000Z
DTEND:20200716T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/40
DESCRIPTION:Title: On the Muskat problem with data in critical Sobolev spaces.\nby Om
ar Lazar (University of Seville) as part of PDE seminar via Zoom\n\n\nAbst
ract\nThe Muskat problem is a nonlinear and nonlocal equation that models
the dynamics of the interface of two incompressible and immiscible fluids
separated by a porous media. I will present a recent global well-posedness
result in critical Sobolev spaces for the 3D Muskat problem that allows t
he 2D interface to be arbitrarily large in the Lipschitz semi-norm (joint
with F. Gancedo).\n\nPlease visit the following link: \nhttps://nguyenquoc
hung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\nto get more informat
ion.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Naber (Northwestern University)
DTSTART:20200716T140000Z
DTEND:20200716T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/41
DESCRIPTION:Title: Ricci Curvature and Differential Harnack Inequalities on Path Space.\nby Aaron Naber (Northwestern University) as part of PDE seminar via Zo
om\n\n\nAbstract\nThere has been an observation of late that many analytic
estimates on manifolds M with lower Ricci curvature bounds have counterpa
rts on the path space PM of the manifold when there are two sided bounds o
n Ricci curvature. We will begin reviewing some of these\, in particular
the estimates of [Nab]\,[Has-Nab] which generalize the Bakry-Emery-Ledoux
estimates to path space. We will then discuss new results\, which are joi
nt with Haslhofer and Knofer\, which generalize the Li-Yau differential ha
rnack inequalities to the path space\, under the assumption of two sided R
icci curvature bounds. \n\nTo accomplish this\, we will introduce a famil
y of Laplace operators on path space PM\, built from finite dimensional t
races of the Markovian hessian\, which we will review. The differential h
arnacks will take the form of differential inequalities for these operator
s\, and will recover the classical Li-Yau when applied the simplest functi
ons on path space\, namely the cylinder functions of one variable.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connor Mooney (University of California\, Irvine)
DTSTART:20200716T150000Z
DTEND:20200716T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/42
DESCRIPTION:Title: The Bernstein problem for elliptic functionals\nby Connor Mooney (
University of California\, Irvine) as part of PDE seminar via Zoom\n\n\nAb
stract\nThe Bernstein problem asks whether entire minimal graphs in $\\mat
hbb{R}^{n+1}$ are necessarily hyperplanes. This problem was completely sol
ved by the late 1960s in combined works of Bernstein\, Fleming\, De Giorgi
\, Almgren\, Simons\, and Bombieri-De Giorgi-Giusti. We will discuss the a
nalogue of this problem for more general elliptic functionals\, and some r
ecent progress in the case n = 6.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduard Feireisl (Czech Technical University\, Prague)
DTSTART:20200723T130000Z
DTEND:20200723T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/43
DESCRIPTION:Title: Ergodic theory for energetically open compressible fluid flows\nby
Eduard Feireisl (Czech Technical University\, Prague) as part of PDE semi
nar via Zoom\n\n\nAbstract\nThe ergodic hypothesis is examined for energet
ically open fluid systems represented by the barotropic Navier--Stokes equ
ations with general inflow/outflow boundary conditions.\n\nAny globally bo
unded trajectory generates a stationary statistical solution\,\n\nwhich is
interpreted as a stochastic process with continuous trajectories supporte
d by the family of weak solutions of the problem. The abstract Birkhoff--K
hinchin theorem is applied to obtain convergence (in expectation and a.s.)
of ergodic averages for any bounded Borel measurable function of state va
riables associated to any stationary solution. Finally\, we show that vali
dity of the ergodic hypothesis is determined by the behavior of entire sol
utions.\n\n (joint work with F. Fanelli (Lyon) and M. Hofmanova (Bielefeld
))\n
LOCATION:https://stable.researchseminars.org/talk/IMS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuang Miao (Wuhan University)
DTSTART:20200723T140000Z
DTEND:20200723T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/44
DESCRIPTION:Title: On the free boundary hard phase fluid in Minkowski spacetime\nby S
huang Miao (Wuhan University) as part of PDE seminar via Zoom\n\n\nAbstrac
t\nI will discuss a recent work on the free boundary hard phase fluid mode
l with Minkowski background. The hard phase model is an idealized model fo
r a relativistic fluid where the sound speed approaches the speed of light
. This work consists of two results: First\, we prove the well-posedness o
f this model in Sobolev spaces. Second\, we give a rigorous justification
of the non-relativistic limit for this model as the speed of light approac
hes infinity. This is joint work with Sohrab Shahshahani and Sijue Wu.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Shkoller (University of California\, Davis)
DTSTART:20200723T150000Z
DTEND:20200723T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/45
DESCRIPTION:Title: Shock Formation for the 3d Euler Equations\nby Steve Shkoller (Uni
versity of California\, Davis) as part of PDE seminar via Zoom\n\n\nAbstra
ct\nTogether with Tristan Buckmaster and Vlad Vicol\, we give a constructi
ve proof of the shock formation process for the 3d Euler equations with vo
rticity. Specifically\, we prove that there exist smooth solutions which
form a generic stable shock with explicitly computable blow up time\, loca
tion\, and direction. The cusp-type solution at blow up is obtained by pro
ving stability of a generic blowup profile in modulated self-similar vari
ables. The stability analysis controls the delicate interaction of wave f
amilies using pointwise bounds along Lagrangian trajectories\, geometric
vorticity structure\, and high-order energy estimates in Sobolev spaces.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toumo Kuusi (University of Helsinki)
DTSTART:20200730T130000Z
DTEND:20200730T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/46
DESCRIPTION:Title: Higher-order linearization and regularity in nonlinear homogenization<
/a>\nby Toumo Kuusi (University of Helsinki) as part of PDE seminar via Zo
om\n\n\nAbstract\nThe analysis of higher-order linearized equations lets u
s develop an incisive large-scale higher regularity theory for solutions o
f nonlinear elliptic equations in the context of homogenization. We procee
d in analogy to the role of the Schauder theory in resolving Hilbert’s 1
9th problem on the regularity of solutions to nonlinear equations with smo
oth coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yao Yao (Georgia Institute of Technology)
DTSTART:20200730T140000Z
DTEND:20200730T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/47
DESCRIPTION:Title: Aggregation-diffusion equation: symmetry\, uniqueness and non-uniquene
ss of steady states\nby Yao Yao (Georgia Institute of Technology) as p
art of PDE seminar via Zoom\n\n\nAbstract\nThe aggregation-diffusion equat
ion is a nonlocal PDE driven by two competing effects: local repulsion mod
eled by nonlinear diffusion\, and long-range attraction modeled by nonloca
l interaction. I will talk about how this equation arises in modeling the
collective motion of cells\, and discuss several qualitative properties of
its steady states and dynamical solutions. Using continuous Steiner symme
trization techniques\, we show that all steady states are radially symmetr
ic up to a translation. (joint work with Carrillo\, Hittmeir and Volzone).
In a recent work\, we further investigate whether they are unique within
the radial class\, and show that for a given mass\, uniqueness/non-uniquen
ess of steady states are determined by the power of the degenerate diffusi
on\, with the critical power being m = 2. (joint work with Delgadino and Y
an.)\n
LOCATION:https://stable.researchseminars.org/talk/IMS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Gómez-Serrano (Princeton University)
DTSTART:20200730T150000Z
DTEND:20200730T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/48
DESCRIPTION:Title: Symmetry in stationary and uniformly rotating solutions of active scal
ars\nby Javier Gómez-Serrano (Princeton University) as part of PDE se
minar via Zoom\n\n\nAbstract\nIn this talk\, I will discuss a Liouville ty
pe theorem for stationary or uniformly-rotating solutions of 2D Euler and
the surface quasi-geostrophic (SQG) equations. The main question we want t
o address is whether every stationary/uniformly-rotating solution must\n b
e radially symmetric\, if the vorticity is compactly supported. Based\n on
joint work with Jaemin Park\, Jia Shi and Yao Yao.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chanwoo Kim (University of Wisconsin-Madison)
DTSTART:20200820T140000Z
DTEND:20200820T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/49
DESCRIPTION:Title: Incompressible Euler limit from Boltzmann equation with Boundary\n
by Chanwoo Kim (University of Wisconsin-Madison) as part of PDE seminar vi
a Zoom\n\n\nAbstract\nA rigorous derivation of the incompressible Euler eq
uations with the no-penetration boundary condition from the Boltzmann equa
tion with the diffuse reflection boundary condition has been a challenging
open problem. We settle this open question in the affirmative when the in
itial data of fluid are well-prepared in a real analytic space\, in 3D hal
f space. As a key of this advance we capture the Navier-Stokes equations s
atisfying the no-slip boundary condition\, as an intermediary approximatio
n of the Euler equations through a new Hilbert-type expansion of the Boltz
mann equation with the diffuse reflection boundary condition. Aiming to ju
stify the approximation we establish a novel quantitative $L^p-L^\\infty$
estimate of the Boltzmann perturbation around a local Maxwellian of such v
iscous approximation\, along with the commutator estimates and the integra
bility gain of the hydrodynamic part in various spaces\; we also establish
direct estimates of the Navier-Stokes equations in higher regularity with
the aid of the initial- boundary and boundary layer weights using a recen
t Green’s function approach. The incompressible Euler limit follows as a
byproduct of our framework.\n\nhttps://nguyenquochung1241.wixsite.com/qhu
ng/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tataru (University of California Berkeley)
DTSTART:20200820T150000Z
DTEND:20200820T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/50
DESCRIPTION:Title: Compressible Euler with physical vacuum: an Eulerian approach\nby
Daniel Tataru (University of California Berkeley) as part of PDE seminar v
ia Zoom\n\n\nAbstract\nThe compressible Euler equation with physical vacu
um is a free boundary problem in gas dynamics\, where the moving boundary
represents the interface between gas and vacuum states\, with the density
decaying to zero at the boundary. Such problems have been traditionally s
tudied using a Lagrangian approach and at high regularity. In this work we
propose a comprehensive alternative approach\, fully within the Eulerian
setting\, and which leads to sharp results. This is joint work with Mihael
a Ifrim\; the extension of these results to the relativistic case is also
joint with Marcelo Disconzi.\n\nhttps://nguyenquochung1241.wixsite.com/qhu
ng/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (Courant Institute of Mathematical Sciences)
DTSTART:20200827T130000Z
DTEND:20200827T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/51
DESCRIPTION:Title: Mean-Field limits for Coulomb-type dynamics\nby Sylvia Serfaty (Co
urant Institute of Mathematical Sciences) as part of PDE seminar via Zoom\
n\n\nAbstract\nWe consider a system of N particles evolving according to t
he gradient flow of their Coulomb or Riesz interaction\, or a similar cons
ervative flow\, and possible added random diffusion. By Riesz interaction\
, we mean inverse power s of the distance with s between d-2 and d where d
denotes the dimension. We present a convergence result as N tends to infi
nity to the expected limiting mean field evolution equation. We also discu
ss the derivation of Vlasov-Poisson from newtonian dynamics in the monokin
etic case\, as well as related results for Ginzburg-Landau vortex dynamics
.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoo
m\n
LOCATION:https://stable.researchseminars.org/talk/IMS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihaela Ifrim (University of Wisconsin-Madison)
DTSTART:20200827T140000Z
DTEND:20200827T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/52
DESCRIPTION:Title: Two dimensional gravity waves at low regularity I: Energy estimates\nby Mihaela Ifrim (University of Wisconsin-Madison) as part of PDE semin
ar via Zoom\n\n\nAbstract\nThis article represents the first installment o
f a series of papers concerned with low regularity solutions for the water
wave equations in two space dimensions. Our focus here is on sharp cubic
energy estimates. Precisely\, we introduce and develop the techniques to p
rove a new class of energy estimates\, which we call \\emph{balanced cubic
estimates}. This yields a key improvement over the earlier cubic estimate
s of Hunter-Ifrim-Tataru [12]\, while preserving their scale invariant cha
racter and their position-velocity potential holomorphic coordinate formul
ation. Even without using any Strichartz estimates\, these results allow u
s to significantly lower the Sobolev regularity threshold for local well-p
osedness\, drastically improving earlier results obtained by Alazard-Burq-
Zuily [3\, 4]\, Hunter-Ifrim-Tataru [12] and Ai [2]. This is joint work wi
th Albert Ai and Daniel Tataru.\n\nhttps://nguyenquochung1241.wixsite.com/
qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Blumenthal (Georgia Institute of Technology)
DTSTART:20200903T130000Z
DTEND:20200903T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/53
DESCRIPTION:Title: Lagrangian Chaos\, Scalar Mixing\, and passive scalar turbulence for m
odels in fluid mechanics\nby Alex Blumenthal (Georgia Institute of Tec
hnology) as part of PDE seminar via Zoom\n\n\nAbstract\nIn models of fluid
mechanics\, Lagrangian flow $\\phi^t$ on the fluid domain describes the m
otion of a passive particle advected by the fluid. It is anticipated that
typically\, Lagrangian flow $\\phi^t$ is chaotic in the sense of (1) sensi
tivity with respect to initial conditions and (2) fast mixing of passive s
calars (equivalently $H^{-1}$ decay for passive scalars). I will present j
oint work with Jacob Bedrossian (U Maryland) and Sam Punshon-Smith (Brown
U) in which we rigorously verify these chaotic properties for various inco
mpressible and stochastically forced fluid models on the periodic box\, in
cluding stochastic 2D Navier-Stokes and hyperviscous 3D Navier-Stokes. I w
ill also present our recent application of these result to the study of pa
ssive scalar turbulence in the Batchelor regime\, i.e.\, the steady state
of passive scalars in a fluid (at fixed viscosity) attained as molecular d
iffusivity goes to 0. In this setting\, we are able to prove Batchelor's i
nverse power law for the power spectrum\, the passive scalar analogue of K
olmogorov's $-4/3$ law for the power spectrum in the inertial range of a t
urbulent 3D fluid.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pd
e-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Lannes (Institut de Mathématiques de Bordeaux\, Universit
é de Bordeaux)
DTSTART:20200903T140000Z
DTEND:20200903T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/54
DESCRIPTION:Title: Floating objects and dispersive perturbations of hyperbolic initial bo
undary value problems\nby David Lannes (Institut de Mathématiques de
Bordeaux\, Université de Bordeaux) as part of PDE seminar via Zoom\n\n\n
Abstract\nWe will show in this talk how some models for the description of
the interactions of waves with floating structures can be formulated as h
yperbolic initial boundary value problems or (depending on the model chose
n for the propagation of the waves)\, dispersive perturbations of such pro
blems.\n\n\nAfter recalling some classical results on hyperbolic initial b
oundary value problems (in particular on the nature of the admissible boun
dary conditions)\, we will explain how the presence of a dispersive pertur
bation in the equations drastically changes the nature of the equations. T
hese different behaviors raise several questions\, one of which being natu
re of the dispersionless limit. We will show that the presence of dispersi
ve boundary layers make this limit singular\, and explain how to control t
hem on an example motivated by a model for wave-structure interactions.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Vega (BCAM - Basque Center for Applied Mathematics)
DTSTART:20200910T130000Z
DTEND:20200910T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/55
DESCRIPTION:Title: The Vortex Filament Equation\, the Talbot effect\, and non-circular je
ts\nby Luis Vega (BCAM - Basque Center for Applied Mathematics) as par
t of PDE seminar via Zoom\n\n\nAbstract\nWe will propose the vortex filame
nt equation as a possible toy model for turbulence\, in particular because
of its striking similarity to the dynamics of non-circular jets. This sim
ilarity implies the existence of some type of Talbot effect due to the int
eraction of non-linear waves that propagate along the filament. Another co
nsequence of this interaction is the existence of a new class of multi-fra
ctal sets that can be seen as a generalization of the graph of Riemann’s
non-differentiable function. Theoretical and numerical arguments about th
e transfer of energy will be also given. This a joint work with V. Banica
and F. de la Hoz.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Krieger (Ecole polytechnique fédérale de Lausanne (EPFL)
)
DTSTART:20200910T140000Z
DTEND:20200910T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/56
DESCRIPTION:Title: Stability of critical Wave Maps blow up beyond the co-rotational setti
ng\nby Joachim Krieger (Ecole polytechnique fédérale de Lausanne (EP
FL)) as part of PDE seminar via Zoom\n\n\nAbstract\nI will discuss recent
work by Miao\, Schlag and myself which establishes a strong stability (and
in fact rigidity) result for certain of the blow up solutions for critica
l Wave Maps mapping into the sphere constructed by K.-Schlag-Tataru. The r
esult is consistent with work by Duyckaerts-Jia-Kenig-Merle\, and the meth
ods are presumably of much wider applicability.\n\nhttps://nguyenquochung1
241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Rousset (Université Paris-Sud)
DTSTART:20200917T130000Z
DTEND:20200917T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/57
DESCRIPTION:by Frédéric Rousset (Université Paris-Sud) as part of PDE s
eminar via Zoom\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IMS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Germain (Courant Institute of Mathematical Sciences)
DTSTART:20200917T140000Z
DTEND:20200917T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/58
DESCRIPTION:Title: Vortex filament solutions for the Navier-Stokes equations\nby Pier
re Germain (Courant Institute of Mathematical Sciences) as part of PDE sem
inar via Zoom\n\n\nAbstract\nI will present a construction of solutions of
the Navier-Stokes equations for data whose vorticity are concentrated on
1D curves (as measures). This corresponds to large locally self-similar da
ta\, for which the usual perturbative approach to local well-posedness doe
s not apply\, and for which a number of interesting questions arise. These
data are also of fundamental importance from a physical perspective\, sin
ce vortex filaments are expected to play a crucial role in 3D flows.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helge Holden (Norwegian University of Science and Technology)
DTSTART:20200924T130000Z
DTEND:20200924T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/59
DESCRIPTION:Title: A Lipschitz metric for the Camassa-Holm equation\nby Helge Holden
(Norwegian University of Science and Technology) as part of PDE seminar vi
a Zoom\n\n\nAbstract\nThe Camassa—Holm equation\n\n$$\n\nu_t+uu_x+p_x=0\
, \\quad p-p_{xx}= u^2+1/2 u_x^2\n\n$$\n\nhas received considerable atten
tion since it was first studied by Camassa and Holm in 1993. Part of the i
nterest stems from the fact that the solution develops singularities in fi
nite time while keeping the $H^1$ norm finite. At wave breaking uniquenes
s is lost as the there are infinitely many ways to extend the solution bey
ond wave breaking. We study the so-called conservative solutions and show
how to construct a Lipschitz metric comparing two conservative solutions.\
n\n\nThis is joint work with J. A. Carrillo (Imperial) and K. Grunert (NTN
U).\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-z
oom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Dodson (Johns Hopkins University)
DTSTART:20200924T140000Z
DTEND:20200924T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/60
DESCRIPTION:Title: Global well-posedness for the cubic NLS with data in a critical Sobole
v space\nby Benjamin Dodson (Johns Hopkins University) as part of PDE
seminar via Zoom\n\n\nAbstract\nIn this talk discuss global well-posedness
for the cubic nonlinear Schrodinger equation with initial data in a criti
cal Sobolev space. We do not require any symmetry on the initial data. The
proof uses decomposition into a finite energy part and a free solution pa
rt.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (Institute for Advanced Study\, Princeton)
DTSTART:20201001T140000Z
DTEND:20201001T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/61
DESCRIPTION:Title: Survey on decoupling\nby Hong Wang (Institute for Advanced Study\,
Princeton) as part of PDE seminar via Zoom\n\n\nAbstract\nIn 2014\, Bourg
ain and Demeter proved the $l^2$--decoupling conjecture for the paraboloid
\, which leads to many developments in harmonic analysis. We are going to
discuss some ideas of decoupling and how people use them.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford University)
DTSTART:20201001T150000Z
DTEND:20201001T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/62
DESCRIPTION:by Eugenia Malinnikova (Stanford University) as part of PDE se
minar via Zoom\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IMS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea R. Nahmod (University of Massachusetts)
DTSTART:20201008T130000Z
DTEND:20201008T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/63
DESCRIPTION:Title: Invariant Gibbs measures and global strong solutions for periodic 2D n
onlinear Schrödinger equations.\nby Andrea R. Nahmod (University of M
assachusetts) as part of PDE seminar via Zoom\n\n\nAbstract\nIn this talk
we will first give a quick background overview of Bourgain's approach to p
rove the invariance of the Gibbs measure for the periodic cubic nonlinear
Schrodinger equation in 2D and of Gubinelli-Imkeller and Perkowski's para-
controlled calculus for parabolic stochastic equations. \nWe will then pre
sent our resolution of the long-standing problem of proving almost sure gl
obal well-posedness (i.e. existence with uniqueness) for the periodic non
linear Schrödinger equation (NLS) in 2D on the support of the Gibbs measu
re\, for any (defocusing and renormalized) odd power nonlinearity. Consequ
ently we get the invariance of the Gibbs measure. This is achieved by a ne
w method we call random averaging operators which precisely captures the i
ntrinsic randomness structure of the problematic high-low frequency intera
ctions at the heart of this NLS problem. \n\n\nThis is joint work with Yu
Deng (USC) and Haitian Yue (USC).\n
LOCATION:https://stable.researchseminars.org/talk/IMS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-marc DELORT (Université Paris 13)
DTSTART:20201008T140000Z
DTEND:20201008T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/64
DESCRIPTION:Title: Long time dispersive estimates for perturbations of a kink solution of
one dimensional cubic wave equations.\nby Jean-marc DELORT (Universit
é Paris 13) as part of PDE seminar via Zoom\n\n\nAbstract\nA kink is a st
ationary solution to a cubic one dimensional wave equation $(\\partial_t^2
-\\partial_x^2)\\phi =\\phi-\\phi^3$ that has different limits when $x$ go
es to $-\\infty$ and $+\\infty$\, like $H(x) =\\tanh(x/\\sqrt{2})$. Asympt
otic\n\nstability of this solution under small odd perturbation in the e
nergy space has been studied in a recent work of Kowalczyk\, Martel and Mu
\\~noz. They have been able to show that the perturbation may be written a
s the sum $a(t)Y(x) +\\psi(t\,x)$\, where $Y$ is a function in Schwartz sp
ace\, $a(t)$ a function of time having some decay properties at\n\ninfinit
y\, and $\\psi(t\,x)$ satisfies some local in space dispersive estimate.\n
\n\nThe main result in this talk gives\, for small odd perturbations of t
he kink that are\n\nsmooth enough and have some space decay\, explicit rat
es of decay for $a(t)$ and for $\\psi(t\,x)$ in the whole space-time domai
n intersected by a strip $\\abs{t}\\leq \\epsilon^{-4+c}$\, for any $c>0$\
, where $\\epsilon$ is the size of the initial\n\nperturbation. \n\n\nThis
is joint work with Nader Masmoudi.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grenier Emmanuel (ENS de Lyon)
DTSTART:20201022T130000Z
DTEND:20201022T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/65
DESCRIPTION:Title: On the instability of viscous boundary layers\nby Grenier Emmanuel
(ENS de Lyon) as part of PDE seminar via Zoom\n\n\nAbstract\nPrandtl boun
dary layers appear when we study the Navier Stokes equations near a bounda
ry as the viscosity goes to zero. The aim of this talk is to review some r
ecents on the instability of such layers (joint work with Y. Guo and T. Ng
uyen)\n
LOCATION:https://stable.researchseminars.org/talk/IMS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Gérard (Université Paris-Saclay)
DTSTART:20201022T140000Z
DTEND:20201022T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/66
DESCRIPTION:Title: Integrability of the Benjamin--Ono equation and applications\nby P
atrick Gérard (Université Paris-Saclay) as part of PDE seminar via Zoom\
n\n\nAbstract\nI will review recent results about the dynamics of the Benj
amin--Ono equation on the torus : sharp wellposedness in the Sobolev space
s\, almost periodicity of solutions\, stability of traveling waves\, exis
tence of singular time periodic solutions. All these results are obtained
as consequences of the construction of a nonlinear Fourier transformation
which is inherited from the Lax pair structure of the equation. I will s
ketch the construction of this transformation and discuss work in progress
about it.\n\nThis talk is based on a series of joint works with Thomas K
appeler (Zuerich) and Peter Topalov (Boston).\n
LOCATION:https://stable.researchseminars.org/talk/IMS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Visan (University of California\, Los Angeles.)
DTSTART:20201029T150000Z
DTEND:20201029T155000Z
DTSTAMP:20260404T111001Z
UID:IMS/67
DESCRIPTION:Title: Recent progress on well-posedness for integrable PDE\nby Monica Vi
san (University of California\, Los Angeles.) as part of PDE seminar via Z
oom\n\n\nAbstract\nI will present the new method developed in joint work w
ith Killip for proving optimal well-posedness for integrable PDE. I will
first discuss this method in the context of the Korteweg-de Vries equation
. I will then discuss subsequent developments (joint with Harrop-Griffith
s and Killip) that have led to optimal well-posedness results for the inte
grable nonlinear Schrodinger and the modified Korteweg-de Vries equations.
\n
LOCATION:https://stable.researchseminars.org/talk/IMS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Figalli (ETH Zurich)
DTSTART:20201105T140000Z
DTEND:20201105T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/68
DESCRIPTION:Title: Stable solutions to semilinear elliptic equations\nby Alessio Figa
lli (ETH Zurich) as part of PDE seminar via Zoom\n\n\nAbstract\nStable sol
utions to semilinear elliptic PDEs appear in several problems. It is known
since the 1970’s that\, in dimension n > 9\, there exist singular stabl
e solutions. In this talk I will describe a recent work with Cabr\\'e\, Ro
s-Oton\, and Serra\, where we prove that stable solutions in dimension n
≤ 9 are smooth. This answers also a famous open problem posed by Brezis\
, concerning the regularity of extremal solutions to the Gelfand problem.\
n
LOCATION:https://stable.researchseminars.org/talk/IMS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renjun Duan (The Chinese University of Hong Kong)
DTSTART:20201112T130000Z
DTEND:20201112T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/69
DESCRIPTION:Title: The Boltzmann equation for uniform shear flow\nby Renjun Duan (The
Chinese University of Hong Kong) as part of PDE seminar via Zoom\n\n\nAbs
tract\nThe uniform shear flow for the rarefied gas is governed by the time
-dependent spatially homogeneous Boltzmann equation with a linear shear fo
rce. The main feature of such flow is that the temperature may increase in
time due to the shearing motion that induces viscous heat and the system
becomes far from equilibrium. For Maxwell molecules\, we establish the uni
que existence\, regularity\, shear-rate-dependent structure and non-negati
vity of self-similar profiles for any small shear rate. The non-negativity
is justified through the large time asymptotic stability even in spatiall
y inhomogeneous perturbation framework\, and the exponential rates of conv
ergence are also obtained with the size proportional to the second order s
hear rate. The analysis supports the numerical result that the self-simila
r profile admits an algebraic high-velocity tail that is the key difficult
y to overcome in the proof. This work is joint with Shuangqian Liu.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Merle (Université de Cergy Pontoise and IHES)
DTSTART:20201119T130000Z
DTEND:20201119T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/70
DESCRIPTION:Title: On the implosion of a three dimensional compressible fluid\nby Fra
nk Merle (Université de Cergy Pontoise and IHES) as part of PDE seminar v
ia Zoom\n\n\nAbstract\nWe consider the compressible three dimensional Navi
er Stokes and Euler equations. In a suitable regime of barotropic laws\, w
e construct a set of finite energy smooth initial data for which the corre
sponding solutions to both equations implode (with infinite density) at a
later time at a point\, and completely describe the associated formation o
f singularity.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Constantin (Princeton University)
DTSTART:20201203T130000Z
DTEND:20201203T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/71
DESCRIPTION:Title: On the Nernst-Planck-Navier-Stokes Equations\nby Peter Constantin
(Princeton University) as part of PDE seminar via Zoom\n\n\nAbstract\nWe r
eview recent results concerning the NPNS system in 2D and 3D.\n\nThe main
results are global stability and regularity results in 2D\, strong nonline
ar stability of Boltzmann states in 3D and unconditional global existence
and regularity in 3D for large data for the NP-Stokes equations\, and cond
itional on regularity of velocity for NPNS\, in the\n\nspecific case of tw
o ionic species with arbitrary diffusivities and the case of N ionic speci
es with equal diffusivities. We obtain interior electroneutrality in the l
imit of vanishing Debye length in the stable cases.\n\n\nThis is joint wor
k with M. Ignatova and F-N. Lee.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose A. Carrillo (University of Oxford)
DTSTART:20210107T140000Z
DTEND:20210107T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/72
DESCRIPTION:Title: The Landau equation: Particle Methods & Gradient Flow Structure\nb
y Jose A. Carrillo (University of Oxford) as part of PDE seminar via Zoom\
n\n\nAbstract\nThe Landau equation introduced by Landau in the 1930's is a
n important partial differential equation in kinetic theory. It gives a de
scription of colliding particles in plasma physics\, and it can be formall
y derived as a limit of the Boltzmann equation where grazing collisions ar
e dominant. The purpose of this talk is to propose a new perspective inspi
red from gradient flows for weak solutions of the Landau equation\, which
is in analogy with the relationship of the heat equation and the 2-Wassers
tein metric gradient flow of the Boltzmann entropy. Moreover\, we aim at u
sing this interpretation to derive a deterministic particle method to solv
e efficiently the Landau equation. Our deterministic particle scheme prese
rves all the conserved quantities at the semidiscrete level for the regula
rized Landau equation and that is entropy decreasing. We will illustrate t
he performance of these schemes with efficient computations using treecode
approaches borrowed from multipole expansion methods for the 3D relevant
Coulomb case. From the theoretical viewpoint\, we use the theory of metric
measure spaces for the Landau equation by introducing a bespoke Landau di
stance $d_L$. Moreover\, we show for a regularized version of the Landau e
quation that we can construct gradient flow solutions\, curves of maximal
slope\, via the corresponding variational scheme. The main result obtained
for the Landau equation shows that the chain rule can be rigorously prove
d for the grazing continuity equation\, this implies that H-solutions with
certain apriori estimates on moments and entropy dissipation are equivale
nt to gradient flow solutions of the Landau equation. We crucially make us
e of estimates on Fisher information-like quantities in terms of the Landa
u entropy dissipation developed by Desvillettes.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Seeger (University of Wisconsin-Madison)
DTSTART:20201217T140000Z
DTEND:20201217T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/73
DESCRIPTION:Title: Lp improving bounds for spherical maximal operators\nby Andreas Se
eger (University of Wisconsin-Madison) as part of PDE seminar via Zoom\n\n
\nAbstract\nConsider maximal operators for spherical means where the dilat
ions are\n\nrestricted to a given subset of a compact interval. We discuss
Lp improving\n\nestimates for such operators and connections to related g
lobal problems.\n\nThe results depend on various notions of fractal dimens
ion of the dilation\n\nset or subsets of it. There are some unexpected res
ults on the shape of the\n\npossible type set. This is joint work with Jor
is Roos\, and also relates to earlier work with\n\nTheresa Anderson\, Kevi
n Hughes and Joris Roos.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Gancedo (University of Seville)
DTSTART:20210114T130000Z
DTEND:20210114T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/74
DESCRIPTION:Title: Two global-in-time results for Muskat\nby Francisco Gancedo (Unive
rsity of Seville) as part of PDE seminar via Zoom\n\n\nAbstract\nIn this t
alk we consider the Muskat problem\, modeling the dynamics of two incompre
ssible immiscible fluids in porous media. First\, we consider fluids of di
fferent densities. This case has been extensively studied recently\, in pa
rticular because its very interesting features. The fluids can be stable\,
enter into unstable regime and next to develop finite time singularities.
We show that this scenario is not possible in 3D for arbitrary slope and
small data\, providing global-in-time critical solutions. Second\, we deal
with capillarity forces with viscosity-density fluids. This case is funda
mental in order to understand fingering phenomena. For gravity unstable si
tuations\, we show that 2D bubbles exist for all time for initial data giv
en by a wide balance between small norm\, density\, viscosity and surface
tension.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Cameron (Courant Institute\, NYU)
DTSTART:20210121T130000Z
DTEND:20210121T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/75
DESCRIPTION:Title: Global Existence for the 3D Muskat problem\nby Stephen Cameron (Co
urant Institute\, NYU) as part of PDE seminar via Zoom\n\n\nAbstract\nThe
Muskat problem studies the evolution of the interface between two incompre
ssible\, immiscible fluids in a porous media. In the case that the fluids
have equal viscosity and the interface is graphical\, this system reduces
to a single nonlinear\, nonlocal parabolic equation for the parametrizati
on. Even in this stable regime\, wave turning can occur leading to finite
time blowup for the slope of the interface. Before that blowup though\,
we prove that an imperfect comparison principle still holds. Using this\,
we are able to show that solutions exist for all time so long as either t
he initial slope is not too large\, or the slope stays bounded for a suffi
ciently long time.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (IAS\, Princeton)
DTSTART:20210311T140000Z
DTEND:20210311T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/76
DESCRIPTION:Title: Local smoothing for the wave equation in 2+1 dimensions\nby Ruixia
ng Zhang (IAS\, Princeton) as part of PDE seminar via Zoom\n\n\nAbstract\n
Sogge's local smoothing conjecture for the wave equation predicts that the
local L^p space-time estimate gains a fractional derivative of order almo
st 1/p compared to the fixed time L^p estimates\, when p>2n/(n-1). Jointly
with Larry Guth and Hong Wang\, we recently proved the conjecture in R^{2
+1}. I will talk about our proof and explain several important ingredients
such as induction on scales and an incidence type theorem.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna L. Mazzucato (Penn State University)
DTSTART:20210325T130000Z
DTEND:20210325T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/77
DESCRIPTION:Title: Mixing\, irregular transport\, and enhanced dissipation\nby Anna L
. Mazzucato (Penn State University) as part of PDE seminar via Zoom\n\n\nA
bstract\nI will discuss transport of passive scalars by incompressible flo
ws and measures of optimal mixing and stirring. I will give two applicatio
ns \, one is an example of complete loss of regularity for solution to lin
ear transport equations\, the others is a global existence result for the
advective Kuramoto-Sivashinsky equation in 2 space dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David M. Ambrose (Drexel University)
DTSTART:20210408T130000Z
DTEND:20210408T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/78
DESCRIPTION:Title: Global existence results for the 2D Kuramoto-Sivashinsky equation\
nby David M. Ambrose (Drexel University) as part of PDE seminar via Zoom\n
\n\nAbstract\nThe Kuramoto-Sivashinsky equation is a model for the motion
of flame fronts. In one spatial dimension much is understood\, including
that solutions exist for all time. Analagous results in two dimensions ar
e much more limited\; most results in 2D assume that the domain is "thin\,
" or approximately one-dimensional. We will give an overview of the resul
ts in one dimension and of anisotropic results in two dimensions. We will
then show some global existence theorems for small data in two dimensions
without making use of any anisotropy. This includes joint work with Anna
Mazzucato.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Yan Li (Rutgers University)
DTSTART:20210506T140000Z
DTEND:20210506T145000Z
DTSTAMP:20260404T111001Z
UID:IMS/79
DESCRIPTION:Title: Regular solutions of the stationary Navier-Stokes equations on high di
mensional Euclidean space\nby Yan Yan Li (Rutgers University) as part
of PDE seminar via Zoom\n\n\nAbstract\nWe study the existence of regular s
olutions of the incompressible stationary Navier-Stokes equations in n-dim
ensional Euclidean space with a given bounded external force of compact su
pport. In dimensions $n\\le 5$\, the existence of such solutions was known
. In this paper\, we extend it to dimensions $n\\le 15$. This is a join
t work with Zhuolun Yang.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Tice (Carnegie Mellon University)
DTSTART:20210513T130000Z
DTEND:20210513T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/80
DESCRIPTION:Title: Traveling wave solutions to the free boundary Navier-Stokes equations<
/a>\nby Ian Tice (Carnegie Mellon University) as part of PDE seminar via Z
oom\n\n\nAbstract\nConsider a layer of viscous incompressible fluid bounde
d below by a flat rigid boundary and above by a moving boundary. The fluid
is subject to gravity\, surface tension\, and an external stress that is
stationary when viewed in a coordinate system moving at a constant velocit
y parallel to the lower boundary. The latter can model\, for instance\, a
tube blowing air on the fluid while translating across the surface. In thi
s talk we will detail the construction of traveling wave solutions to this
problem\, which are themselves stationary in the same translating coordin
ate system. While such traveling wave solutions to the Euler equations are
well-known\, to the best of our knowledge this is the first construction
of such solutions with viscosity. This is joint work with Giovanni Leoni.\
n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\
n
LOCATION:https://stable.researchseminars.org/talk/IMS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zaher Hani (University of Michigan)
DTSTART:20210520T130000Z
DTEND:20210520T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/81
DESCRIPTION:Title: Full derivation of the wave kinetic equation\nby Zaher Hani (Unive
rsity of Michigan) as part of PDE seminar via Zoom\n\n\nAbstract\nWe will
discuss a recent work\, in collaboration with Yu Deng (USC)\, in which we
provide the rigorous derivation of the wave kinetic equation from the cubi
c nonlinear Schrödinger (NLS) equation at the kinetic timescale\, under a
particular scaling law that describes the limiting process. This solves a
main conjecture in the theory of wave turbulence\, i.e. the kinetic theor
y of nonlinear wave systems. Our result is the wave analog of Lanford's th
eorem on the derivation of the Boltzmann kinetic equation from particle sy
stems\, where in both cases one takes the thermodynamic limit as the size
of the system diverges to infinity\, and as the interaction strength of wa
ves or radius of particles vanishes to 0\, according to some specified sca
ling law. This is the first result of its kind for any nonlinear wave syst
em.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Rosenzweig (MIT)
DTSTART:20211028T130000Z
DTEND:20211028T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/82
DESCRIPTION:Title: Global solutions of aggregation equations and other flows with random
diffusion\nby Matthew Rosenzweig (MIT) as part of PDE seminar via Zoom
\n\n\nAbstract\nAggregation equations\, such as the parabolic-elliptic Pat
lak-Keller-Segel model\, are known to have an optimal threshold for global
existence vs. finite-time blow-up. In particular\, if the diffusion is ab
sent\, then all smooth solutions with finite second moment can exist only
locally in time. Nevertheless\, one can ask whether global existence can b
e restored by adding a suitable noise to the equation\, so that the dynami
cs are now stochastic. In this talk\, we investigate whether random diffus
ion can restore global existence for a large class of active scalar equati
ons in arbitrary dimension with possibly singular velocity fields. This cl
ass includes Hamiltonian flows\, such as the SQG equation and its generali
zations\, and gradient flows\, such as those arising in aggregation models
. For this class\, we show global existence of solutions in Gevrey-type Fo
urier-Lebesgue spaces with quantifiable high probability.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Louis Marzuola (University of North Carolina at Chapel Hill
)
DTSTART:20211104T130000Z
DTEND:20211104T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/83
DESCRIPTION:Title: On 4th order nonlinear thin-film like PDEs describing crystal surface
evolution\nby Jeremy Louis Marzuola (University of North Carolina at C
hapel Hill) as part of PDE seminar via Zoom\n\n\nAbstract\nWe discuss rece
nt results with a number of collaborators on PDEs relating to the relaxati
on of a crystal surface. After a brief overview of the motivating microsc
opic process that leads to the models\, we will present results on the wel
l-posedness of these models in various settings. Towards the end\, we wil
l show numerical evidence to motivate a number of open questions about thi
s family of models.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Spolaor (UC San Diego)
DTSTART:20211111T130000Z
DTEND:20211111T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/84
DESCRIPTION:Title: (Quasi-)conformal methods in two-dimensional free boundary problems\nby Luca Spolaor (UC San Diego) as part of PDE seminar via Zoom\n\n\nAbs
tract\nAbstract: In this talk I will explain how to obtain precise informa
tions on the structure of the free-boundary to $2$-dimensional solutions o
f the one and two phase problems at so-called branching points using the t
heory of (quasi-)conformal maps. The talk is based on joint work with G. D
e Philippis (Courant) and B. Velichkov (Pisa).\n
LOCATION:https://stable.researchseminars.org/talk/IMS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mingione (University of Parma)
DTSTART:20211118T130000Z
DTEND:20211118T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/85
DESCRIPTION:Title: Perturbations beyond Schauder\nby Giuseppe Mingione (University of
Parma) as part of PDE seminar via Zoom\n\n\nAbstract\nSo-called Schauder
estimates are a standard tool in the analysis of linear elliptic and parab
olic PDEs. They had been originally proved by Hopf (1929\, interior case)\
, and by Schauder and Caccioppoli (1934\, global estimates). Since then\,
several proofs were given (Campanato\, Trudinger\, Simon). The nonlinear c
ase is a more recent achievement from the 80s (Giaquinta & Giusti\, Ivert\
, J. Manfredi\, Lieberman). All these classical results take place in the
uniformly elliptic case. I will discuss progress in the nonuniformly ellip
tic one.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helena J Nussenzveig Lopes (Universidade Federal do Rio de Janeiro
)
DTSTART:20211202T130000Z
DTEND:20211202T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/86
DESCRIPTION:Title: 2D Navier-Stokes equations on a bounded domain with holes and Navier f
riction boundary conditions\nby Helena J Nussenzveig Lopes (Universida
de Federal do Rio de Janeiro) as part of PDE seminar via Zoom\n\n\nAbstrac
t\nWe will discuss the large time behavior of solutions of 2D Navier-Stoke
s in bounded domains which are not necessarily simply connected\, when we
impose Navier friction boundary conditions. We establish exponential time
decay\, for both velocity and vorticity\, under various assumptions on the
friction coefficient relative to curvature of the boundary\, for differen
t types of domains. We also discuss the special role\, played by the disk
and the annulus\, in this analysis. This is joint work with Christophe Lac
ave\, Milton Lopes Filho and Jim Kelliher.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh Binh Tran (Southern Methodist University)
DTSTART:20211216T130000Z
DTEND:20211216T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/87
DESCRIPTION:Title: Some Recent Results On Wave Turbulence: Derivation\, Analysis\, Numer
ics and Physical Application\nby Minh Binh Tran (Southern Methodist Un
iversity) as part of PDE seminar via Zoom\n\n\nAbstract\nWave turbulence
describes the dynamics of both classical and non-classical nonlinear waves
out of thermal equilibrium. In this talk\, we will discuss some of our
recent results on some aspects of wave turbulence\, concerning the derivat
ion and analysis of wave kinetic equations\, some numerical algorithms and
physical applications in Bose-Einstein Condensates.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Terracini (Università di Torino)
DTSTART:20220127T130000Z
DTEND:20220127T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/88
DESCRIPTION:Title: Free boundaries in segregation problems\nby Susanna Terracini (Uni
versità di Torino) as part of PDE seminar via Zoom\n\nAbstract: TBA\n\nht
tps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://stable.researchseminars.org/talk/IMS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongjie Dong (Brown University)
DTSTART:20220210T130000Z
DTEND:20220210T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/89
DESCRIPTION:Title: Sobolev estimates for fractional PDEs\nby Hongjie Dong (Brown Univ
ersity) as part of PDE seminar via Zoom\n\n\nAbstract\nI will discuss some
recent results on Sobolev estimates for fractional elliptic and parabolic
equations with or without weights. We considered equations with time frac
tional derivatives of the Caputo type\, or with nonlocal derivatives in th
e space variables\, or both. This is based on joint work with Doyoon Kim (
Korea University) and Yanze Liu (Brown).\n
LOCATION:https://stable.researchseminars.org/talk/IMS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan-Vasile Matioc (Universität Regensburg)
DTSTART:20220224T130000Z
DTEND:20220224T135000Z
DTSTAMP:20260404T111001Z
UID:IMS/90
DESCRIPTION:Title: The two-phase quasi-stationary Stokes flow by capillarity in the plane
\nby Bogdan-Vasile Matioc (Universität Regensburg) as part of PDE sem
inar via Zoom\n\n\nAbstract\nWe discuss a two-phase moving boundary proble
m that describes the two-dimensional quasistationary Stokes flow of two fl
uids with different densities and viscosities that occupy the entire plane
in the regime where surface tension effects are taken into account at the
interface that separates the fluids. In this setting the classical method
s of potential theory can be used to transform the model into a nonlinear
and nonlocal evolution problem for the function that parameterizes the int
erface between the fluids\, the nonlinearities being expressed by singular
integral operators. This problem is of parabolic type\, well-posed in all
Sobolev spaces up to critical regularity\, and it features some parabolic
smoothing properties. Joint work with Georg Prokert.\n
LOCATION:https://stable.researchseminars.org/talk/IMS/90/
END:VEVENT
END:VCALENDAR