Difference between revisions of "PDE Geometric Analysis seminar"

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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2016 | Tentative schedule for Fall 2017]]===
+
===[[Fall 2020-Spring 2021 | Tentative schedule for Fall 2020-Spring 2021]]===
 +
 
 +
== PDE GA Seminar Schedule Fall 2019-Spring 2020 ==
  
= PDE GA Seminar Schedule Spring 2017 =
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 10: Line 11:
 
!align="left" | speaker
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | title
!align="left" | host(s)
+
!style="width:20%" align="left" | host(s)
 +
|- 
 +
|Sep 9
 +
| Scott Smith (UW Madison)
 +
|[[#Scott Smith | Recent progress on singular, quasi-linear stochastic PDE ]]
 +
| Kim and Tran
 +
|- 
 +
|Sep 14-15
 +
|
 +
|[[ # |AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html  ]]
 +
 +
|- 
 +
|Sep 23
 +
| Son Tu (UW Madison)
 +
|[[#Son Tu | State-Constraint static Hamilton-Jacobi equations in nested domains ]]
 +
| Kim and Tran
 +
|- 
 +
|Sep 28-29, VV901
 +
|  https://www.ki-net.umd.edu/content/conf?event_id=993
 +
|  |  Recent progress in analytical aspects of kinetic equations and related fluid models 
 +
 +
|- 
 +
|Oct 7
 +
| Jin Woo Jang (Postech)
 +
|[[#Jin Woo Jang| On a Cauchy problem for the Landau-Boltzmann equation ]]
 +
| Kim
 +
|- 
 +
|Oct 14
 +
| Stefania Patrizi (UT Austin)
 +
|[[#Stefania Patrizi | Dislocations dynamics: from microscopic models to macroscopic crystal plasticity ]]
 +
| Tran
 +
|- 
 +
|Oct 21
 +
| 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 ]]
 +
| Li
 +
|- 
 +
|Oct 25-27, VV901
 +
| https://www.ki-net.umd.edu/content/conf?event_id=1015
 +
||  Forward and Inverse Problems in Kinetic Theory
 +
| Li
 +
|-
 +
|Oct 28
 +
| Albert Ai (UW Madison)
 +
|[[#Albert Ai | TBA ]]
 +
| Ifrim
 +
|- 
 +
|Nov 4
 +
| Yunbai Cao (UW Madison)
 +
|[[#Yunbai Cao | TBA ]]
 +
| Kim and Tran
 +
|- 
 +
|Nov 11
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|Nov 18
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 
|-
 
|-
|#date
+
|Nov 25
| #speaker
+
| Mathew Langford (UT Knoxville)
|[[#  |   #title ]]
+
|[[#Speaker | TBA ]]
| #host
+
| Angenent
|-
+
|
|-
+
|- 
|January 23 (Special time and location: 3-3:50pm, B325 Van Vleck)
+
|Feb 17
| Sigurd Angenent (UW)
+
| Yannick Sire (JHU)
|[[# Sigurd Angenent | Ancient convex solutions to Mean Curvature Flow]]
+
|[[#Yannick Sire (JHU) | TBA ]]
| Local
+
| Tran
|-  
+
|- 
 +
|Feb 24
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|-  
 +
|March 2
 +
| Theodora Bourni (UT Knoxville)
 +
|[[#Speaker | TBA ]]
 +
| Angenent
 +
|- 
 +
|March 9
 +
| Ian Tice (CMU)
 +
|[[#Ian Tice| TBA ]]
 +
| Kim
 +
|-
 +
|March 16
 +
| No seminar (spring break)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|-
 +
|March 23
 +
| Jared Speck (Vanderbilt)
 +
|[[#Jared Speck | TBA ]]
 +
| SCHRECKER
 +
|- 
 +
|March 30
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|April 6
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|April 13
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|-
 +
|April 20
 +
| Hyunju Kwon (IAS)
 +
|[[#Hyunju Kwon | TBA ]]
 +
| Kim
 +
|- 
 +
|April 27
 +
| Speaker (Institute)
 +
|[[#Speaker | TBA ]]
 +
| Host
 +
|- 
 +
|May 18-21
 +
| Madison Workshop in PDE 2020
 +
|[[#Speaker | TBA ]]
 +
| Tran
 +
|}
 +
 
 +
== Abstracts ==
 +
 
 +
===Scott Smith===
 +
 
 +
Title: Recent progress on singular, quasi-linear stochastic PDE
 +
 
 +
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.
  
|-
 
|January 30
 
| Serguei Denissov (UW)
 
|[[# Serguei Denissov | ]]
 
| Local
 
|-
 
  
 +
===Son Tu===
  
|-
+
Title: State-Constraint static Hamilton-Jacobi equations in nested domains
|February 6
 
| Benoit Perthame (University of Paris VI)
 
|[[#| ]]
 
| Wasow lecture
 
|-  
 
  
 +
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).
  
|-
 
|February 13
 
| Bing Wang (UW)
 
|[[# Bing Wang | ]]
 
| Local
 
|-
 
  
|-
+
===Jin Woo Jang===
|February 20
 
| Hans-Joachim Hein (Fordham)
 
|[[# Hans-Joachim Hein | ]]
 
| Viaclovsky
 
|-
 
  
|-
+
Title: On a Cauchy problem for the Landau-Boltzmann equation
|February 27
 
| Ben Seeger (University of Chicago)
 
|[[#Ben Seeger | ]]
 
| Tran
 
|-  
 
  
|-
+
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.
|March 7 - Applied math/PDE/Analysis seminar
 
| Roger Temam (Indiana University)
 
|[[#| ]]
 
| Mathematics Department Distinguished Lecture
 
|-  
 
  
  
|-
+
===Stefania Patrizi===
|March 8 - Applied math/PDE/Analysis seminar
 
| Roger Temam (Indiana University) 
 
|[[#| ]]
 
| Mathematics Department Distinguished Lecture
 
|-
 
  
|-
+
Title:
|March 13
+
Dislocations dynamics: from microscopic models to macroscopic crystal plasticity
| Sona Akopian (UT-Austin)
 
|[[#Sona Akopian | ]]
 
| Kim
 
  
|-
+
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.
|March 27
 
| Sylvia Serfaty (Courant)
 
|[[#Sylvia Serfaty | ]]
 
| Tran
 
  
|-
 
|March 29
 
| Sylvia Serfaty (Courant)
 
|[[#Sylvia Serfaty | ]]
 
| Wasow lecture
 
  
|-
+
===Claude Bardos===
|April 3
+
Title: From the d'Alembert paradox to the 1984 Kato criteria via the 1941 $1/3$ Kolmogorov law and the 1949 Onsager conjecture
| Zhenfu Wang (Maryland)
 
|[[#Zhenfu Wang | ]]
 
| Kim
 
  
|-
+
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.
|May 1st
 
| Jeffrey Streets (UC-Irvine)
 
|[[#Jeffrey Streets | ]]
 
| Bing Wang
 
|}
 
  
=Abstracts=
+
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.
  
=== ===
+
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.
====Sigurd Angenent====
 
The Huisken-Hamilton-Gage theorem on compact convex solutions to MCF shows that in forward time all solutions do the same thing, namely, they shrink to a point and become round as they do so.  Even though MCF is ill-posed in backward time there do exist solutions that are defined for all t<0 , and one can try to classify all such &ldquo;Ancient solutions.&rdquo;  In doing so one finds that there is interesting dynamics associated to Ancient solutions. I will discuss what is currently known about these solutions.  Some of the talk is based on joint work with Sesum and Daskalopoulos.
 

Latest revision as of 13:45, 15 October 2019

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 2020-Spring 2021

PDE GA Seminar Schedule Fall 2019-Spring 2020

date speaker title host(s)
Sep 9 Scott Smith (UW Madison) Recent progress on singular, quasi-linear stochastic PDE Kim and Tran
Sep 14-15 AMS Fall Central Sectional Meeting https://www.ams.org/meetings/sectional/2267_program.html
Sep 23 Son Tu (UW Madison) State-Constraint static Hamilton-Jacobi equations in nested domains Kim and Tran
Sep 28-29, VV901 https://www.ki-net.umd.edu/content/conf?event_id=993 Recent progress in analytical aspects of kinetic equations and related fluid models
Oct 7 Jin Woo Jang (Postech) On a Cauchy problem for the Landau-Boltzmann equation Kim
Oct 14 Stefania Patrizi (UT Austin) Dislocations dynamics: from microscopic models to macroscopic crystal plasticity Tran
Oct 21 Claude Bardos (Université Paris Denis Diderot, France) From d'Alembert paradox to 1984 Kato criteria via 1941 1/3 Kolmogorov law and 1949 Onsager conjecture Li
Oct 25-27, VV901 https://www.ki-net.umd.edu/content/conf?event_id=1015 Forward and Inverse Problems in Kinetic Theory Li
Oct 28 Albert Ai (UW Madison) TBA Ifrim
Nov 4 Yunbai Cao (UW Madison) TBA Kim and Tran
Nov 11 Speaker (Institute) TBA Host
Nov 18 Speaker (Institute) TBA Host
Nov 25 Mathew Langford (UT Knoxville) TBA Angenent
Feb 17 Yannick Sire (JHU) TBA Tran
Feb 24 Speaker (Institute) TBA Host
March 2 Theodora Bourni (UT Knoxville) TBA Angenent
March 9 Ian Tice (CMU) TBA Kim
March 16 No seminar (spring break) TBA Host
March 23 Jared Speck (Vanderbilt) TBA SCHRECKER
March 30 Speaker (Institute) TBA Host
April 6 Speaker (Institute) TBA Host
April 13 Speaker (Institute) TBA Host
April 20 Hyunju Kwon (IAS) TBA Kim
April 27 Speaker (Institute) TBA Host
May 18-21 Madison Workshop in PDE 2020 TBA Tran

Abstracts

Scott Smith

Title: Recent progress on singular, quasi-linear stochastic PDE

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.


Son Tu

Title: State-Constraint static Hamilton-Jacobi equations in nested domains

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).


Jin Woo Jang

Title: On a Cauchy problem for the Landau-Boltzmann equation

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

Title: 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.


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.

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.

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.