Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Fall 2018-Spring 2019)
(PDE GA Seminar Schedule Fall 2020-Spring 2021)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===
+
===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==
 
  
  
{| cellpadding="8"
+
== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==
!style="width:20%" align="left" | date 
+
Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. 
!align="left" | speaker
 
!align="left" | title
 
!style="width:20%" align="left" | host(s)
 
  
|- 
+
'''Week 1 (9/1/2020-9/5/2020)'''
|August 31 (FRIDAY),
 
| Julian Lopez-Gomez (Complutense University of Madrid)
 
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]
 
| Rabinowitz
 
  
|- 
+
1. Paul Rabinowitz - The calculus of variations and phase transition problems.
|September 10,
+

https://www.youtube.com/watch?v=vs3rd8RPosA
| Hiroyoshi Mitake (University of Tokyo)
 
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]
 
| Tran
 
|- 
 
|September 12 and September 14,
 
| Gunther Uhlmann (UWash)
 
|[[#Gunther Uhlmann | TBA ]]
 
| Li
 
|- 
 
|September 17,
 
| Changyou Wang (Purdue)
 
|[[#Changyou Wang |  Some recent results on mathematical analysis of Ericksen-Leslie System ]]
 
| Tran
 
|-
 
|Sep 28, Colloquium
 
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
 
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
 
| Thiffeault
 
|-
 
|October 1,
 
| Matthew Schrecker (UW)
 
|[[#Matthew Schrecker | Finite energy methods for the 1D isentropic Euler equations ]]
 
| Kim and Tran
 
|- 
 
|October 8,
 
| Anna Mazzucato (PSU)
 
|[[#Anna Mazzucato | On the vanishing viscosity limit in incompressible flows ]]
 
| Li and Kim
 
|- 
 
|October 15,
 
| Lei Wu (Lehigh)
 
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]
 
| Kim
 
|- 
 
|October 22,
 
| Annalaura Stingo (UCD)
 
|[[#Annalaura Stingo | Global existence of small solutions to a model wave-Klein-Gordon system in 2D ]]
 
| Mihaela Ifrim
 
|- 
 
|October 29,
 
| Yeon-Eung Kim (UW)
 
|[[#Yeon-Eung Kim | Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties ]]
 
| Kim and Tran
 
|- 
 
|November 5,
 
| Albert Ai (UC Berkeley)
 
|[[#Albert Ai | Low Regularity Solutions for Gravity Water Waves ]]
 
| Mihaela Ifrim
 
|- 
 
|Nov 7 (Wednesday), Colloquium
 
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)
 
|[[#Nov 7: Luca Spolaor (MIT) |  (Log)-Epiperimetric Inequality and the Regularity of Variational Problems  ]]
 
| Feldman
 
|-
 
|December 3, ''' Time: 3:00, Room: B223 Van Vleck '''
 
| Trevor Leslie (UW)
 
|[[#Trevor Leslie | Flocking Models with Singular Interaction Kernels ]]
 
| Kim and Tran
 
|-
 
|December 10, ''' Time: 2:25, Room: B223 Van Vleck '''
 
|Serena Federico (MIT)
 
|[[#Serena Federico | Sufficient conditions for local solvability of some degenerate partial differential operators ]]
 
| Mihaela Ifrim
 
|-
 
|December 10, Colloquium, '''Time: 4:00'''
 
| [https://math.mit.edu/~maxe/ Max Engelstein] (MIT)
 
|[[#Max Engelstein| The role of Energy in Regularity ]]
 
| Feldman
 
|-
 
|January 28,
 
| Ru-Yu Lai (Minnesota)
 
|[[#Ru-Yu Lai | Inverse transport theory and related applications ]]
 
| Li and Kim
 
|-
 
| February 4,
 
|
 
|[[# | No seminar (several relevant colloquiums in Feb/5 and Feb/8)]]
 
|
 
|-
 
| February 11,
 
| Seokbae Yun (SKKU, long term visitor of UW-Madison)
 
|[[# Seokbae Yun | The propagations of uniform upper bounds fo the spatially homogeneous relativistic Boltzmann equation]]
 
| Kim
 
|-
 
| February 13 '''4PM''',
 
| Dean Baskin (Texas A&M)
 
|[[#Dean Baskin | Radiation fields for wave equations]]
 
| Colloquium
 
|- 
 
| February 18,  '''3:30PM, Room: VV B239'''
 
| Daniel Tataru (Berkeley)
 
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]
 
| Ifrim
 
|-                                                                                                                                                         
 
| February 19, '''Time: 4-5PM, Room: VV B139'''
 
| Wenjia Jing (Tsinghua University)
 
|[[#Wenjia Jing | Periodic homogenization of Dirichlet problems in perforated domains: a unified proof ]]
 
| Tran
 
|-
 
|February 25,
 
| Xiaoqin Guo (UW)
 
|[[#Xiaoqin Guo | Quantitative homogenization in a balanced random environment ]]
 
| Kim and Tran
 
|-
 
|March 4 '''time:4PM-5PM, Room: VV B239'''
 
| Vladimir Sverak (Minnesota)
 
|[[#Vladimir Sverak | Wasow lecture "PDE aspects of the Navier-Stokes equations and simpler models" ]]
 
| Kim
 
|-   
 
|March 11
 
| Jonathan Luk (Stanford)
 
|[[#Jonathan Luk | Stability of vacuum for the Landau equation with moderately soft potentials  ]]
 
| Kim
 
|-
 
|March 12, '''4:00 p.m. in VV B139'''
 
| Trevor Leslie (UW-Madison)
 
|[[# Trevor Leslie| TBA ]]
 
| Analysis seminar
 
|-
 
|March 18,
 
| Spring recess (Mar 16-24, 2019)
 
|[[#  |  ]]
 
 
|-
 
|March 25
 
| Jiaxin Jin
 
|[[# Jiaxin Jin  |Convergence to the complex balanced equilibrium for some reaction-diffusion systems with boundary equilibria.  ]]
 
| local speaker
 
|-   
 
|April 1
 
| Zaher Hani (Michigan)
 
|[[#Zaher Hani | TBA  ]]
 
| Ifrim
 
|-   
 
|April 8 
 
| Jingrui Cheng (Stony Brook)
 
|[[#Jingrui Cheng | Gradient estimate for complex Monge-Ampere equations ]]
 
| Feldman
 
|-
 
|April 15,
 
| Yao Yao (Gatech)
 
|[[#Yao Yao | Radial symmetry of stationary and uniformly-rotating solutions in 2D incompressible fluid equations ]]
 
| Tran
 
|-   
 
|April 22,
 
| Jessica Lin (McGill University)
 
|[[#Jessica Lin | TBA ]]
 
| Tran
 
|- 
 
|April 29,
 
| Beomjun Choi (Columbia)
 
|[[#Beomjun Choi  | Evolution of non-compact hypersurfaces by inverse mean curvature]]
 
|  Angenent
 
|}
 
  
== Abstracts ==
+
2. Frank Merle - On the implosion of a three dimensional compressible fluid.
 +
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 
  
===Julian Lopez-Gomez===
+
'''Week 2 (9/6/2020-9/12/2020)'''
  
Title: The theorem of characterization of the Strong Maximum Principle
+
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.
 +
https://www.youtube.com/watch?v=4ndtUh38AU0
  
Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes  a popular result of Berestycki, Nirenberg and Varadhan.
+
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI
  
===Hiroyoshi Mitake===
 
Title: On approximation of time-fractional fully nonlinear equations
 
  
Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.)
 
  
 +
'''Week 3 (9/13/2020-9/19/2020)'''
  
 +
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ
  
===Changyou Wang===
+
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE
  
Title: Some recent results on mathematical analysis of Ericksen-Leslie System
 
  
Abstract: The Ericksen-Leslie system is the governing equation  that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.
 
  
===Matthew Schrecker===
+
'''Week 4 (9/20/2020-9/26/2020)'''
  
Title: Finite energy methods for the 1D isentropic Euler equations
+
1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be
  
Abstract: In this talk, I will present some recent results concerning the 1D isentropic Euler equations using the theory of compensated compactness in the framework of finite energy solutions. In particular, I will discuss the convergence of the vanishing viscosity limit of the compressible Navier-Stokes equations to the Euler equations in one space dimension. I will also discuss how the techniques developed for this problem can be applied to the existence theory for the spherically symmetric Euler equations and the transonic nozzle problem. One feature of these three problems is the lack of a priori estimates in the space $L^\infty$, which prevent the application of the standard theory for the 1D Euler equations.
+
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM
  
===Anna Mazzucato===
 
  
Title: On the vanishing viscosity limit in incompressible flows
 
  
Abstract: I will discuss recent results on the  analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity  may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions.  I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.
+
'''Week 5 (9/27/2020-10/03/2020)'''
  
===Lei Wu===
+
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo
  
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects
+
2.  Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c
  
Abstract: Hydrodynamic limits concern the rigorous derivation of fluid equations from kinetic theory. In bounded domains, kinetic boundary corrections (i.e. boundary layers) play a crucial role. In this talk, I will discuss a fresh formulation to characterize the boundary layer with geometric correction, and in particular, its applications in 2D smooth convex domains with in-flow or diffusive boundary conditions. We will focus on some newly developed techniques to justify the asymptotic expansion, e.g. weighted regularity in Milne problems and boundary layer decomposition.
 
  
 +
'''Week 6 (10/04/2020-10/10/2020)'''
  
===Annalaura Stingo===
+
1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E
  
Title: Global existence of small solutions to a model wave-Klein-Gordon system in 2D
+
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing
 +
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html
  
Abstract: This talk deals with the problem of global existence of solutions to a quadratic coupled wave-Klein-Gordon system in space dimension 2, when initial data are small, smooth and mildly decaying at infinity.Some physical models, especially related to general relativity, have shown the importance of studying such systems. At present, most of the existing results concern the 3-dimensional case or that of compactly supported initial data. We content ourselves here with studying the case of a model quadratic quasi-linear non-linearity, that expresses in terms of « null forms »  .
 
Our aim is to obtain some energy estimates on the solution when some Klainerman vector fields are acting on it, and sharp uniform estimates. The former ones are recovered making systematically use of normal forms’ arguments for quasi-linear equations, in their para-differential version, whereas we derive the latter ones by deducing a system of ordinary differential equations from the starting partial differential system. We hope this strategy will lead us in the future to treat the case of the most general non-linearities.
 
  
===Yeon-Eung Kim===
+
'''Week 7 (10/11/2020-10/17/2020)'''
  
Title: Construction of solutions to a Hamilton-Jacobi equation with a maximum constraint and some uniqueness properties
+
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s
  
A biological evolution model involving trait as space variable has a interesting feature phenomena called Dirac concentration of density as diffusion coefficient vanishes. The limiting equation from the model can be formulated by Hamilton Jacobi equation with a maximum constraint. In this talk, I will present a way of constructing a solution to a constraint Hamilton Jacobi equation together with some uniqueness and non-uniqueness properties.
+
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg
  
===Albert Ai===
 
  
Title: Low Regularity Solutions for Gravity Water Waves
+
'''Week 8 (10/18/2020-10/24/2020)'''
  
Abstract: We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness below that which is attainable by energy estimates alone. Using a paradifferential reduction of Alazard-Burq-Zuily and low regularity Strichartz estimates, we apply this idea to the well-posedness of the gravity water waves equations in arbitrary space dimension. Further, in two space dimensions, we discuss how one can apply local smoothing effects to further extend this result.
+
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg
  
===Trevor Leslie===
+
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ
  
Title: Flocking Models with Singular Interaction Kernels
+
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.
  
Abstract: Many biological systems exhibit the property of self-organization, the defining feature of which is coherent, large-scale motion arising from underlying short-range interactions between the agents that make up the system.  In this talk, we give an overview of some simple models that have been used to describe the so-called flocking phenomenon.  Within the family of models that we consider (of which the Cucker-Smale model is the canonical example), writing down the relevant set of equations amounts to choosing a kernel that governs the interaction between agents.  We focus on the recent line of research that treats the case where the interaction kernel is singular.  In particular, we discuss some new results on the wellposedness and long-time dynamics of the Euler Alignment model and the Shvydkoy-Tadmor model.
 
  
===Serena Federico===
+
'''Week 9 (10/25/2020-10/31/2020)'''
  
Title: Sufficient conditions for local solvability of some degenerate partial differential operators
+
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE
  
Abstract: In  this  talk  we  will  give  sufficient  conditions  for the local  solvability  of  a  class  of degenerate second order linear partial differential operators with smooth coefficients. The class under consideration, inspired by some generalizations of the Kannai operator, is characterized by the presence of a complex subprincipal symbol. By giving suitable conditions on the subprincipal part and using the technique of a priori estimates,  we will show that the operators in the class are at least $L^2$ to $L^2$ locally solvable.
+
2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764
  
===Max Engelstein===
 
  
Title: The role of Energy in Regularity
 
  
Abstract: The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to ``nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy.
+
'''Week 10 (11/1/2020-11/7/2020)'''
  
However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field.
+
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be
  
We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur.
+
2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html
  
  
===Ru-Yu Lai===
 
Title: Inverse transport theory and related applications.
 
  
Abstract: The inverse transport problem consists of reconstructing the optical properties of a medium from boundary measurements. It finds applications in a variety of fields. In particular, radiative transfer equation (a linear transport equation) models the photon propagation in a medium in optical tomography. In this talk we will address results on the determination of these optical parameters. Moreover, the connection between the inverse transport problem and the Calderon problem will also be discussed.
+
'''Week 11 (11/8/2020-11/14/2020)'''
  
===Seokbae Yun===
+
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc
Title: The propagations of uniform upper bounds fo the spatially homogeneous relativistic Boltzmann equation
 
  
Abstract: In this talk, we consider the propagation of the uniform upper bounds
+
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0
for the spatially homogenous relativistic Boltzmann equation. For this, we establish two
 
types of estimates for the the gain part of the collision operator: namely, a potential
 
type estimate and a relativistic hyper-surface integral estimate. We then combine them
 
using the relativistic counter-part of the Carlemann representation to derive a uniform
 
control of the gain part, which gives the desired propagation of the uniform bounds of
 
the solution. Some applications of the results are also considered. This is a joint work
 
with Jin Woo Jang and Robert M. Strain.
 
  
  
 +
'''Week 12 (11/15/2020-11/21/2020)'''
  
===Daniel Tataru===
+
1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY
  
Title: A Morawetz inequality for water waves.
+
2.  Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk
  
Authors: Thomas Alazard, Mihaela Ifrim, Daniel Tataru.
 
  
Abstract: We consider gravity water waves in two space dimensions, with finite or infinite depth. Assuming some uniform scale invariant Sobolev bounds for the solutions, we prove local energy decay (Morawetz) estimates globally in time. Our result is uniform in the infinite depth limit.
+
'''Week 13 (11/22/2020-11/28/2020)'''
  
 +
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be
  
===Wenjia Jing===
+
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8
  
Title: Periodic homogenization of Dirichlet problems in perforated domains: a unified proof
+
'''Week 14 (11/29/2020-12/5/2020)'''
  
Abstract: In this talk, we present a unified proof to establish periodic homogenization for the Dirichlet problems associated to the Laplace operator in perforated domains; here the uniformity is with respect to the ratio between scaling factors of the perforation holes and the periodicity. Our method recovers, for critical scaling of the hole-cell ratio, the “strange term coming from nowhere” found by Cioranescu and Murat, and it works at the same time for other settings of hole-cell ratios. Moreover, the method is naturally based on analysis of rescaled cell problems and hence reveals the intrinsic connections among the apparently different homogenization behaviors in those different settings. We also show how to quantify the approach to get error estimates and corrector results.
+
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations,  
 +
https://youtu.be/xfAKGc0IEUw
  
  
===Xiaoqin Guo===
+
'''Week 15 (12/6/2020-12/12/2020)'''
  
Title: Quantitative homogenization in a balanced random environment
+
1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be
  
Abstract: Stochastic homogenization of discrete difference operators is closely related to the convergence of random walk in a random environment (RWRE) to its limiting process. In this talk we discuss non-divergence form difference operators in an i.i.d random environment and the corresponding process—a random walk in a balanced random environment in the integer lattice Z^d. We first quantify the ergodicity of the environment viewed from the point of view of the particle. As consequences, we obtain algebraic rates of convergence for the quenched central limit theorem of the RWRE and for the homogenization of both elliptic and parabolic non-divergence form difference operators. Joint work with J. Peterson (Purdue) and H. V. Tran (UW-Madison).
 
  
===Sverak===
+
{| cellpadding="8"
 
+
!style="width:20%" align="left" | date 
Title: PDE aspects of the Navier-Stokes equations and simpler models
+
!align="left" | speaker
 
+
!align="left" | title
Abstract: Does the Navier-Stokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.
+
!style="width:20%" align="left" | host(s)
 
+
|-  
===Jonathan Luk===
+
|}
 
 
Title: Stability of vacuum for the Landau equation with moderately soft potentials
 
 
 
Abstract: Consider the Landau equation with moderately soft potentials in the whole space. We prove that sufficiently small and localized regular initial data give rise to unique global-in-time smooth solutions. Moreover, the solutions approach that of the free transport equation as $t\to +\infty$. This is the first stability of vacuum result for a binary collisional kinetic model featuring a long-range interaction.
 
 
 
 
 
===Jiaxin Jin===
 
 
 
Title: Convergence to the complex balanced equilibrium for some reaction-diffusion systems with boundary equilibria.
 
 
 
Abstract: We first analyze a three-species system with boundary equilibria in some stoichiometric classes and study the rate of convergence to the complex balanced equilibrium. Then we prove similar results on the convergence to the positive equilibrium for a fairly general two-species reversible reaction-diffusion network with boundary equilibria.
 
 
 
===Jingrui Cheng===
 
 
 
Title: Gradient estimate for complex Monge-Ampere equations
 
 
 
Abstract: We consider complex Monge-Ampere equations on a compact Kahler manifold. Previous gradient estimates of the solution all require some derivative bound of the right hand side. I will talk about how to get gradient estimate in $L^p$ and $L^{\infty}$, depending only on the continuity of the right hand side.
 
  
 +
== Abstracts ==
  
 +
===  ===
  
===Beomjun Choi===
+
Title:  
In this talk, we first introduce the inverse mean curvature flow and its well known application in the the proof of Riemannian Penrose inequality by Huisken and Ilmanen. Then our main result on the existence and behavior of convex non-compact solution will be discussed.  
 
  
The key ingredient is a priori interior in time estimate on the inverse mean curvature in terms of the aperture of supporting cone at infinity. This is a joint work with P. Daskalopoulos and I will also mention the recent work with P.-K. Hung concerning the evolution of singular hypersurfaces.
+
Abstract:

Latest revision as of 07:40, 29 November 2020

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Previous PDE/GA seminars

Tentative schedule for Fall 2021-Spring 2022

PDE GA Seminar Schedule Fall 2020-Spring 2021

Welcome to the new mode of our PDEGA seminar this semester. Each week, we'll introduce to you two talks that are interesting and related to our interests. As the videos are already on Youtube or other platforms, you could choose to watch them whenever you want to; our goal here is merely to pick our favorite ones out of thousands of already available recorded talks. 

Week 1 (9/1/2020-9/5/2020)

1. Paul Rabinowitz - The calculus of variations and phase transition problems. 
https://www.youtube.com/watch?v=vs3rd8RPosA

2. Frank Merle - On the implosion of a three dimensional compressible fluid. https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 

Week 2 (9/6/2020-9/12/2020)

1. Yoshikazu Giga - On large time behavior of growth by birth and spread. https://www.youtube.com/watch?v=4ndtUh38AU0

2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI


Week 3 (9/13/2020-9/19/2020)

1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ

2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE


Week 4 (9/20/2020-9/26/2020)

1. Robert M. Strain - Global mild solutions of the Landau and non-cutoff Boltzmann equation. https://www.youtube.com/watch?v=UWrCItk2euo&feature=youtu.be

2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM


Week 5 (9/27/2020-10/03/2020)

1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo

2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c


Week 6 (10/04/2020-10/10/2020)

1. Felix Otto - The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows. https://www.youtube.com/watch?v=7FQsiZpQA7E

2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html


Week 7 (10/11/2020-10/17/2020)

1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s

2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg


Week 8 (10/18/2020-10/24/2020)

1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg

2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ

Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.


Week 9 (10/25/2020-10/31/2020)

1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE

2. Tristan Buckmaster - Stable shock wave formation for the isentropic compressible Euler equations. https://stanford.zoom.us/rec/play/DwuT8rE-K1uJC0LghYPtsoaNmPBk9-P5EK4ZeWh1mVNJELRHn-ay-gOVXHSTRz_0X3iUZDBoUVYq8zfd.Tuqy8urKY4jESivm?continueMode=true&_x_zm_rtaid=GiRX307iT7encyYgIEgh9Q.1603308889393.b4a9b3af5c64cc9ca735cffbe25d8b7b&_x_zm_rhtaid=764


Week 10 (11/1/2020-11/7/2020)

1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be

2. Luc Nguyen - Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory http://www.birs.ca/events/2017/5-day-workshops/17w5110/videos/watch/201705041518-Nguyen.html


Week 11 (11/8/2020-11/14/2020)

1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc

2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0


Week 12 (11/15/2020-11/21/2020)

1. Irene M. Gamba - Boltzmann type equations in a general framework: from the classical elastic flow, to gas mixtures, polyatomic gases, and more, https://youtu.be/fPlhAMGULtY

2. Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk


Week 13 (11/22/2020-11/28/2020)

1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be

2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8

Week 14 (11/29/2020-12/5/2020)

1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations, https://youtu.be/xfAKGc0IEUw


Week 15 (12/6/2020-12/12/2020)

1. Pierre Gilles Lemarié-Rieusset - On weak solutions of the Navier-Stokes equations with infinite energy, https://www.youtube.com/watch?v=OeFJ6r-GLJc&feature=youtu.be


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