Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Fall 2019-Spring 2020)
(PDE GA Seminar Schedule Fall 2020-Spring 2021)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===
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===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==
 
  
  
{| cellpadding="8"
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== PDE GA Seminar Schedule Fall 2020-Spring 2021 ==
!style="width:20%" align="left" | date 
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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
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!align="left" | title
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'''Week 1 (9/1/2020-9/5/2020)'''
!style="width:20%" align="left" | host(s)
+
 
|-
+
1. Paul Rabinowitz - The calculus of variations and phase transition problems.
|Sep 9
+

https://www.youtube.com/watch?v=vs3rd8RPosA
| Scott Smith (UW Madison)
+
 
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]
+
2. Frank Merle - On the implosion of a three dimensional compressible fluid.
| Kim and Tran
+
https://www.youtube.com/watch?v=5wSNBN0IRdA&feature=youtu.be 
|-
+
 
|Sep 14-15
+
'''Week 2 (9/6/2020-9/12/2020)'''
|
+
 
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html  ]]
+
1. Yoshikazu Giga - On large time behavior of growth by birth and spread.
+
https://www.youtube.com/watch?v=4ndtUh38AU0
|- 
+
 
|Sep 23
+
2. Tarek Elgindi - Singularity formation in incompressible fluids. https://youtu.be/29zUjm7xFlI
| Son Tu (UW Madison)
+
 
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]
+
 
| Kim and Tran
+
 
|- 
+
'''Week 3 (9/13/2020-9/19/2020)'''
|Sep 28-29, VV901
+
 
https://www.ki-net.umd.edu/content/conf?event_id=993
+
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ
|  |  Recent progress in analytical aspects of kinetic equations and related fluid models 
+
 
+
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE
|- 
+
 
|Oct 7
+
 
| Jin Woo Jang (Postech)
+
 
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]
+
'''Week 4 (9/20/2020-9/26/2020)'''
| Kim
+
 
|-
+
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
|Oct 14
+
 
| Stefania Patrizi (UT Austin)
+
2. Elena Kosygina - Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension https://www.youtube.com/watch?v=tVZv0ftT3PM
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]
+
 
| Tran
+
 
|- 
+
 
|Oct 21
+
'''Week 5 (9/27/2020-10/03/2020)'''
| Claude Bardos (Université Paris Denis Diderot, France)
+
 
|[[#Claude Bardos | From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture ]]
+
1. Isabelle Gallagher - From Newton to Boltzmann, fluctuations and large deviations. https://www.youtube.com/watch?v=BkrKkUVadDo
| Li
+
 
|-  
+
2. Connor Mooney - The Bernstein problem for elliptic functionals, https://www.youtube.com/watch?v=lSfnyfCL74c
|Oct 25-27, VV901
+
 
| https://www.ki-net.umd.edu/content/conf?event_id=1015
+
 
||  Forward and Inverse Problems in Kinetic Theory
+
'''Week 6 (10/04/2020-10/10/2020)'''
| Li
+
 
|-  
+
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
|Oct 28
+
 
| Albert Ai (UW Madison)
+
2. Inwon Kim - Evolution of star-shaped sets in Mean curvature flow with forcing
|[[#Albert Ai | Two dimensional gravity waves at low regularity: Energy estimates  ]]
+
http://www.birs.ca/events/2018/5-day-workshops/18w5033/videos/watch/201806190900-Kim.html
| Ifrim
+
 
|-
+
 
|Nov 4
+
'''Week 7 (10/11/2020-10/17/2020)'''
| Yunbai Cao (UW Madison)
+
 
|[[#Yunbai Cao | Vlasov-Poisson-Boltzmann system in Bounded Domains]]
+
1. Benoit Perthame - Multiphase models of living tissues and the Hele-Shaw limit. https://www.youtube.com/watch?v=UGVJnJCfw5s
| Kim and Tran
+
 
|- 
+
2. Yifeng Yu - Properties of Effective Hamiltonians. https://www.youtube.com/watch?v=U06G4wjF-Hg
|Nov 18
+
 
| Ilyas Khan (UW Madison)
+
 
|[[#Ilyas Khan | The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension ]]
+
'''Week 8 (10/18/2020-10/24/2020)'''
| Kim and Tran
+
 
|-
+
1. Carlos Kenig - Asymptotic simplification for solutions of the energy critical nonlinear wave equation. https://youtu.be/jvzUqAxU8Xg
|Nov 25
+
 
| Mathew Langford (UT Knoxville)
+
2. Kyeongsu Choi - Ancient mean curvature flows and singularity analysis. https://www.youtube.com/watch?v=Iu1iLjdFjKQ
|[[#Mathew Langford | Concavity of the arrival time ]]
+
 
| Angenent
+
Virtual Analysis and PDE Seminar (VAPS): https://sites.uci.edu/pdeonlineseminar/. First talk by Ovidiu Savin.
|-  
+
 
|Dec 9 - Colloquium (4-5PM)
+
 
| Hui Yu (Columbia)
+
'''Week 9 (10/25/2020-10/31/2020)'''
|[[#Hui Yu | TBA ]]
+
 
| Tran
+
1. John Ball - Some energy minimization problems for liquid crystals. https://www.youtube.com/watch?v=-j0jc-y7JzE
|-  
+
 
|Feb. 3
+
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
| Philippe LeFloch (Sorbonne University and CNRS)
+
 
|[[#Philippe LeFloch | Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions  ]]
+
 
| Feldman
+
 
|-  
+
'''Week 10 (11/1/2020-11/7/2020)'''
|Feb. 10
+
 
| Joonhyun La (Stanford)
+
1. Sylvia Serfaty - Mean-Field limits for Coulomb-type dynamics. https://www.youtube.com/watch?v=f7iSTnAe808&feature=youtu.be
|[[#Joonhyun La | On a kinetic model of polymeric fluids ]]
+
 
| Kim
+
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
|- 
+
 
|Feb 17
+
 
| Yannick Sire (JHU)
+
 
|[[#Yannick Sire | Minimizers for the thin one-phase free boundary problem ]]
+
'''Week 11 (11/8/2020-11/14/2020)'''
| Tran
+
 
|-
+
1. Andrzej Święch - Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures https://www.youtube.com/watch?v=KC514krtWAc
|Feb 19 - Colloquium (4-5PM)
+
 
| Zhenfu Wang (University of Pennsylvania)
+
2. Alexandru Ionescu - On the nonlinear stability of shear flows and vortices, https://youtu.be/Zt_Izzi87V0
|[[#Zhenfu Wang | Quantitative Methods for the Mean Field Limit Problem ]]
+
 
| Tran
+
 
|-
+
'''Week 12 (11/15/2020-11/21/2020)'''
|Feb 24
+
 
| Matthew Schrecker (UW Madison)
+
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
|[[#Matthew Schrecker | Existence theory and Newtonian limit for 1D relativistic Euler equations ]]
+
 
| Feldman
+
2.  Andrej Zlatos - Euler Equations on General Planar Domains, https://www.youtube.com/watch?v=FdyyMZirRwk
|-
+
 
|March 2
+
 
| Theodora Bourni (UT Knoxville)
+
'''Week 13 (11/22/2020-11/28/2020)'''
|[[#Speaker | TBA ]]
+
 
| Angenent
+
1. Camillo De Lellis - Flows of vector fields: classical and modern, https://www.youtube.com/watch?v=dVXSC3rtvok&feature=youtu.be
|-
+
 
|March 9
+
2. Wilfrid Gangbo - Analytical Aspect of Mean Field Games (Part 1/2), https://www.youtube.com/watch?v=KI5n6OYzzW8
| Ian Tice (CMU)
+
 
|[[#Ian Tice| TBA ]]
+
'''Week 14 (11/29/2020-12/5/2020)'''
| Kim
+
 
|- 
+
1. Juan Dávila - Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations,
|March 16
+
https://youtu.be/xfAKGc0IEUw
| No seminar (spring break)
+
 
|[[#Speaker | TBA ]]
+
2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc
| Host
+
 
|-
+
 
|March 23
+
 
| Jared Speck (Vanderbilt)
+
'''Week 15 (12/6/2020-12/12/2020)'''
|[[#Jared Speck | TBA ]]
+
 
| Schrecker
+
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
|- 
+
 
|March 30
+
2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU
| Huy Nguyen (Brown)
+
 
|[[#Huy Nguyen | TBA ]]
+
 
| organizer
+
'''Spring 2021'''
|-
+
 
|April 6
+
'''Week 1 (1/31/2021- 2/6/2021)'''
| Speaker (Institute)
+
 
|[[#Speaker | TBA ]]
+
1. Emmanuel Grenier -   instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be
| Host
+
 
|-
+
2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84
|April 13
+
 
| Hyunju Kwon (IAS)
+
 
|[[#Hyunju Kwon | TBA ]]
+
'''Week 2 ( 2/7/2021- 2/13/2021)'''
| Kim
+
 
|-
+
1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek
|April 20
+
 
| Adrian Tudorascu (WVU)
+
2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE
|[[#Adrian Tudorascu | On the Lagrangian description of the Sticky Particle flow ]]
+
 
| Feldman
+
Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.
|- 
+
 
|April 27
+
'''Week 3 ( 2/14/2021- 2/20/2021)'''
| Speaker (Institute)
+
 
|[[#Speaker | TBA ]]
+
1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s
| Host
+
 
|-   
+
2. Hao Jia nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg
|May 18-21
+
 
| Madison Workshop in PDE 2020
+
 
|[[#Speaker | TBA ]]
+
 
| Tran
+
'''Week 4 ( 2/21/2021- 2/27/2021)'''
|}
+
 
 +
1. Anne-Laure Dalibard -  Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309
  
== Abstracts ==
+
2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68
  
===Scott Smith===
+
'''Week 5 ( 2/28/2021- 3/6/2021)'''
  
Title: Recent progress on singular, quasi-linear stochastic PDE
+
1. Inwon Kim -  A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317
  
Abstract: This talk with focus on quasi-linear parabolic equations with an irregular forcing . These equations are ill-posed in the traditional sense of distribution theory.  They require flexibility in the notion of solution as well as new a priori bounds.  Drawing on the philosophy of rough paths and regularity structures, we develop the analytic part of a small data solution theory. This is joint work with Felix Otto, Hendrik Weber, and Jonas Sauer.
+
2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k
  
 +
'''Week 6 (3/7/2021-3/13/2021)'''
  
===Son Tu===
+
1. Ondřej Kreml -  Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html
  
Title: State-Constraint static Hamilton-Jacobi equations in nested domains
+
2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c
  
Abstract: We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}$ in $\mathbb R^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k \in \mathbb N$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega=\bigcup_k \Omega_k$. In many cases,  the rates obtained are proven to be optimal (it's a joint work with Yeoneung Kim and Hung V. Tran).
 
  
 +
'''Week 7 (3/14/2021-3/20/2021)'''
  
===Jin Woo Jang===
+
1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM
  
Title: On a Cauchy problem for the Landau-Boltzmann equation
+
2. Alexis Vasseur -  Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html
  
Abstract: In this talk, I will introduce a recent development in the global well-posedness of the Landau equation (1936) in a general smooth bounded domain, which has been a long-outstanding open problem. This work proves the global stability of the Landau equation in an $L^\infty_{x,v}$ framework with the Coulombic potential in a general smooth bounded domain with the specular reflection boundary condition for initial perturbations of the Maxwellian equilibrium states. Our methods consist of the generalization of the well-posedness theory for the kinetic Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (BCM-1996) to further control the velocity derivatives, which ensures the uniqueness. This is a joint work with Y. Guo, H. J. Hwang, and Z. Ouyang.
 
  
  
===Stefania Patrizi===
+
'''Week 8 (3/21/2021- 3/27/2021)'''
  
Title:  
+
1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity
 
  
Abstract: Dislocation theory aims at explaining the plastic behavior of materials by the motion of line defects in crystals. Peierls-Nabarro models consist in approximating the geometric motion of these defects by nonlocal reaction-diffusion equations. We study the asymptotic  limit of  solutions of  Peierls-Nabarro equations. Different scalings lead to different models at microscopic, mesoscopic and macroscopic scale. This is  joint work with E. Valdinoci.
+
2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A
  
  
===Claude Bardos===
 
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture
 
  
Abstract: Several of my recent contributions, with Marie Farge, Edriss Titi, Emile Wiedemann, Piotr and Agneska Gwiadza, were motivated by the following issues: The role of boundary effect in mathematical theory of fluids mechanic and the similarity, in presence of these effects, of the weak convergence in the zero viscosity limit and the statistical theory of turbulence. As a consequence, I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation.
+
'''Week 9 (3/28/2021- 4/3/2021)'''
  
Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and give supplementary condition that imply the global conservation of energy in a domain with boundary and the absence of anomalous energy dissipation in the zero viscosity limit of solutions of the Navier-Stokes equation in the presence of no slip boundary condition.
+
1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM
  
Eventually the above results are compared with  several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations and one may insist on the fact that in such case the the absence of anomalous energy dissipation is {\bf equivalent} to the persistence of regularity in the zero viscosity limit. Eventually this remark contributes to the resolution of the d'Alembert Paradox.
+
2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9
  
===Albert Ai===
 
Title: Two dimensional gravity waves at low regularity: Energy estimates
 
  
Abstract: In this talk, we will consider the gravity water wave equations in two space dimensions. Our focus is on sharp cubic energy estimates and low regularity solutions. Precisely, we will introduce techniques to prove a new class of energy estimates, which we call balanced cubic estimates. This yields a key improvement over the earlier cubic estimates of Hunter-Ifrim-Tataru, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness. This is joint work with Mihaela Ifrim and Daniel Tataru.
+
'''Week 10 (4/4/2021- 4/10/2021)'''
  
===Ilyas Khan===
+
1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235
Title: The Uniqueness of Asymptotically Conical Self-Shrinkers in High Codimension.
 
  
Abstract: In this talk, we will consider self-shrinking solitons of the mean curvature flow that are smoothly asymptotic to a Riemannian cone in $\mathbb{R}^n$. In 2011, L. Wang proved the uniqueness of self-shrinking ends asymptotic to a cone $C$ in the case of hypersurfaces (codimension 1) by using a backwards uniqueness result for the heat equation due to Escauriaza, Sverak, and Seregin. Later, J. Bernstein proved the same fact using purely elliptic methods. We consider the case of self-shrinkers in high codimension, and outline how to prove the same uniqueness result in this significantly more general case, by using geometric arguments and extending Bernstein’s result.
+
2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8
  
===Mathew Langford===
+
'''Week 11(4/11/2021- 4/17/2021)'''
Title: Concavity of the arrival time
 
  
Abstract:  We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a novel concavity maximum principle argument to the corresponding level set flow equations. In particular, this yields a short proof of Hamilton’s differential Harnack inequality for mean curvature flow and, more generally, Andrews’ differential Harnack inequalities for certain “$\alpha$-inverse-concave” flows.
+
1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo
  
===Philippe LeFloch===
+
2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html
Title: Nonlinear stability of self-gravitating matter under low decay and weak regularity conditions
 
  
Abstract:  I will present recent progress on the global evolution problem for self-gravitating matter. (1) For Einstein's constraint equations, motivated by a scheme proposed by Carlotto and Schoen I will show the existence of asymptotically Euclidean Einstein spaces with low decay; joint work with T. Nguyen.
+
'''Week 12(4/18/2021- 4/24/2021)'''
  
(2) For Einstein's evolution equations in the regime near Minkowski spacetime, I will show the global nonlinear stability of massive matter fields; joint work with Y. Ma.  
+
1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0
  
(3) For the colliding gravitational wave problem, I will show the existence of weakly regular spacetimes containing geometric singularities across which junction conditions are imposed; joint work with B. Le Floch and G. Veneziano.
+
2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo
  
 +
'''Week 13(4/25/2021- 5/1/2021)'''
  
===Joonhyun La===
+
1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI
Title: On a kinetic model of polymeric fluids
 
  
Abstract: In this talk, we prove global well-posedness of a system describing behavior of dilute flexible polymeric fluids. This model is based on kinetic theory, and a main difficulty for this system is its multi-scale nature. A new function space, based on moments, is introduced to address this issue, and this function space allows us to deal with larger initial data.
+
2.
  
  
===Yannick Sire===
 
Title: Minimizers for the thin one-phase free boundary problem
 
  
Abstract: We consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will try to describe.
+
{| cellpadding="8"
 +
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|- 
 +
|}
  
===Matthew Schrecker===
+
== Abstracts ==
Title: Existence theory and Newtonian limit for 1D relativistic Euler equations
 
  
Abstract: I will present the results of my recent work with Gui-Qiang Chen on the Euler equations in the conditions of special relativity. I will show how the theory of compensated compactness may be used to obtain the existence of entropy solutions to this system. Moreover, it is expected that as the light speed grows to infinity, solutions to the relativistic Euler equations will converge to their classical (Newtonian) counterparts. The theory we develop is also sufficient to demonstrate this convergence rigorously.
+
=== ===
  
===Adrian Tudorascu===
+
Title:
Title: On the Lagrangian description of the Sticky Particle flow
 
  
Abstract: R. Hynd has recently proved that for absolutely continuous initial velocities the Sticky Particle system admits solutions described by monotone flow maps in Lagrangian coordinates. We present a generalization of this result to general initial velocities and discuss some consequences. (This is based on ongoing work with M. Suder.)
+
Abstract:

Latest revision as of 23:00, 18 April 2021

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

2. Yao Yao - Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states, https://www.youtube.com/watch?v=C_4qCimIMYc


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

2. Albert Fathi - Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation, https://www.youtube.com/watch?v=0y8slhbQlTU


Spring 2021

Week 1 (1/31/2021- 2/6/2021)

1. Emmanuel Grenier - instability of viscous shear layers https://www.youtube.com/watch?v=0_EG4VWIYvU&feature=youtu.be

2. Robert Pego - Dynamics and oscillations in models of coagulation and fragmentation https://www.youtube.com/watch?v=3712lImYP84


Week 2 ( 2/7/2021- 2/13/2021)

1. Ryan Hynd, The Hamilton-Jacobi equation, past and present https://www.youtube.com/watch?v=jR6paJf7aek

2. Jacob Bedrossian - Chaotic mixing of the Lagrangian flow map and the power spectrum of passive scalar turbulence in the Batchelor regime https://youtu.be/3lNQNsdlGTE

Colloquium (2/12/2021): Bobby Wilson (University of Washington). More information can be found here http://www.math.wisc.edu/wiki/index.php/Colloquia.

Week 3 ( 2/14/2021- 2/20/2021)

1. Diogo A. Gomes - Monotone MFGs - theory and numerics https://www.youtube.com/watch?v=lj1L7AHHY3s

2. Hao Jia - nonlinear asymptotic stability in two dimensional incompressible Euler equations https://youtu.be/KMf7K2sTLXg


Week 4 ( 2/21/2021- 2/27/2021)

1. Anne-Laure Dalibard - Boundary layer methods in semilinear fluid equations https://www.msri.org/workshops/944/schedules/29309

2. Gui-Qiang G. Chen - On Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type: Analysis and Connections https://www.youtube.com/watch?v=W3sa-8qtw68

Week 5 ( 2/28/2021- 3/6/2021)

1. Inwon Kim - A variational scheme for Navier-Stokes Equations https://www.msri.org/workshops/944/schedules/29317

2. Robert L. Jerrard - Solutions of the Ginzburg–Landau equatons with vorticity concentrating near a nondegenerate geodesic https://www.youtube.com/watch?v=M0NQh2PET_k

Week 6 (3/7/2021-3/13/2021)

1. Ondřej Kreml - Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial datas https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231027-Kreml.html

2. Rita Ferreira - Homogenization of a stationary mean-field game via two-scale convergence https://www.youtube.com/watch?v=EICMVmt5o9c


Week 7 (3/14/2021-3/20/2021)

1. Sergey Denisov - Small scale formation in 2D Euler dynamics https://www.youtube.com/watch?v=7ffUgTC34tM

2. Alexis Vasseur - Instability of finite time blow-ups for incompressible Euler https://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011231000-Vasseur.html


Week 8 (3/21/2021- 3/27/2021)

1. Peter Sternberg - Variational Models for Phase Transitions in Liquid Crystals Based Upon Disparate Values of the Elastic Constants https://www.youtube.com/watch?v=4rSPsDvkTYs

2. François Golse - Half-space problem for the Boltzmann equation with phase transition at the boundary https://mysnu-my.sharepoint.com/:v:/g/personal/bear0117_seoul_ac_kr/ETGjasFQ7ylHu04qUz4KomYB98uMHLd-q96DOJGwbbEB0A


Week 9 (3/28/2021- 4/3/2021)

1. Susan Friedlander - Kolmogorov, Onsager and a stochastic model for turbulence https://www.youtube.com/watch?v=xk3KZQ-anDM

2. Sergei Chernyshenko - Auxiliary functionals: a path to solving the problem of turbulence https://www.youtube.com/watch?v=NrF7n3MyCy4&list=PLf_ipOSbWC86n18q4JMn_1J04S90FpdeE&index=9


Week 10 (4/4/2021- 4/10/2021)

1. Camillo De Lellis - Transport equations and ODEs with nonsmooth coefficients https://www.msri.org/workshops/945/schedules/29235

2. Weinan E - PDE problems that arise from machine learning https://www.youtube.com/watch?v=5rb8DJkxfg8

Week 11(4/11/2021- 4/17/2021)

1. Marian Gidea - Topological methods and Hamiltonian instability https://youtu.be/aMN7zJZavDo

2. David Gerard-Varet - On the effective viscosity of suspensions http://www.birs.ca/events/2020/5-day-workshops/20w5188/videos/watch/202011230644-Gerard-Varet.html

Week 12(4/18/2021- 4/24/2021)

1. Takis Souganidis - Phase-field models for motion by mean curvature - 1 https://www.youtube.com/watch?v=fH8ygVAZm-0

2. Nader Masmoudi - Inviscid Limit and Prandtl System, https://youtu.be/tLg3HwVDlOo

Week 13(4/25/2021- 5/1/2021)

1. James Stone - Astrophysical fluid dynamics https://youtu.be/SlPSa37QMeI

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Abstracts

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