Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Spring 2018)
(PDE GA Seminar Schedule Fall 2018-Spring 2019)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Fall 2018 | Tentative schedule for Fall 2018]]===
+
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===
  
 
+
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==
 
+
== PDE GA Seminar Schedule Spring 2018 ==
+
  
  
Line 16: Line 14:
  
 
|-   
 
|-   
|January 29, '''3-3:50PM, B341 VV.'''
+
|August 31 (FRIDAY),
| Dan Knopf (UT Austin)
+
| Julian Lopez-Gomez (Complutense University of Madrid)
|[[#Dan Knopf | Non-Kähler Ricci flow singularities that converge to Kähler-Ricci solitons]]
+
|[[#Julian Lopez-Gomez | The theorem of characterization of the Strong Maximum Principle ]]
| Angenent
+
| Rabinowitz
|-  
+
 
|February 5, '''3-3:50PM, B341 VV.'''
+
|-   
| Andreas Seeger (UW)
+
|September 10,
|[[#Andreas Seeger Singular integrals and  a problem on mixing flows ]]
+
| Hiroyoshi Mitake (University of Tokyo)
| Kim & Tran
+
|[[#Hiroyoshi Mitake | On approximation of time-fractional fully nonlinear equations ]]
|-  
+
| Tran
|February 12
+
|-
| Sam Krupa (UT-Austin)
+
|September 12 and September 14,
|[[#Sam Krupa Proving Uniqueness of Solutions for Burgers Equation Entropic for a Single Entropy, with Eye Towards Systems Case ]]
+
| Gunther Uhlmann (UWash)
| Lee
+
|[[#Gunther Uhlmann | TBA ]]
|-  
+
| Li
|February 19
+
|-   
| Maja Taskovic (UPenn)
+
|September 17,
|[[#Maja Taskovic TBD ]]
+
| 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 | TBA ]]
 +
| Li and Kim
 +
|-  
 +
|October 15,
 +
| Lei Wu (Lehigh)
 +
|[[#Lei Wu | Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects ]]
 
| Kim
 
| Kim
 +
|- 
 +
|October 22,
 +
| Annalaura Stingo (UCD)
 +
|[[#Annalaura Stingo | TBA ]]
 +
| Mihaela Ifrim
 +
|- 
 +
|October 29,
 +
| Yeon-Eung Kim (UW)
 +
|[[#Yeon-Eung Kim | TBA ]]
 +
| Kim and Tran
 +
|- 
 +
|November 5,
 +
| Albert Ai (UC Berkeley)
 +
|[[#Albert Ai | TBA ]]
 +
| Mihaela Ifrim
 +
|- 
 +
|December 3,
 +
| Trevor Leslie (UW)
 +
|[[#Trevor Leslie | TBA ]]
 +
| Kim and Tran
 
|-  
 
|-  
|March 5
+
|December 10,
| Khai Nguyen (NCSU)
+
|   ( )
|[[#Khai Nguyen | TBD ]]
+
|[[#  | TBA ]]
| Tran
+
|
 
|-  
 
|-  
|March 12
+
|January 28,
| Hongwei Gao (UCLA)
+
|   ( )
|[[#Hongwei Gao |  TBD ]]
+
|[[# | TBA ]]
 +
|   
 +
|-
 +
|Time: TBD,
 +
| Jessica Lin (McGill University)
 +
|[[#Jessica Lin | TBA ]]
 
| Tran
 
| Tran
|-  
+
|-  
|March 19
+
|March 4
| Huy Nguyen (Princeton)
+
| Vladimir Sverak (Minnesota)
|[[#Huy Nguyen | TBD ]]
+
|[[#Vladimir Sverak | TBA(Wasow lecture) ]]
| Lee
+
| Kim
 
|-
 
|-
|March 24 (Mar 24-Apr 1, 2018)
+
|March 18,
| Spring recess
+
| Spring recess (Mar 16-24, 2019)
|[[#  |  TBD ]]
+
|[[#  |  ]]
 
|   
 
|   
 
|-
 
|-
|April 9
+
|April 29,
| reserved
+
|   ( )
|[[# |  TBD ]]
+
|[[# | TBA ]]
| Tran
+
|   
|-
+
|April 21-22 (Saturday-Sunday)
+
| Midwest PDE seminar
+
|[[#Midwest PDE seminar | ]]
+
| Angenent, Feldman, Kim, Tran.
+
|-
+
|April 25 (Wednesday)
+
| Hitoshi Ishii (Wasow lecture)
+
|[[#Hitoshi Ishii TBD]]
+
| Tran.
+
 
|}
 
|}
  
 
== Abstracts ==
 
== Abstracts ==
  
===Dan Knopf===
+
===Julian Lopez-Gomez===
 +
 
 +
Title: The theorem of characterization of the Strong Maximum Principle
 +
 
 +
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.
 +
 
 +
===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.)
 +
 
 +
 
 +
 
 +
===Changyou Wang===
  
Title: Non-Kähler Ricci flow singularities that converge to Kähler-Ricci solitons
+
Title: Some recent results on mathematical analysis of Ericksen-Leslie System
  
Abstract: We describe Riemannian (non-Kähler) Ricci flow solutions that develop finite-time Type-I singularities whose parabolic dilations converge to a shrinking Kähler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered by Feldman, Ilmanen, and Knopf in 2003. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-Kähler solutions of Ricci flow that become asymptotically Kähler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of Kähler metrics under Ricci flow.
+
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.
  
===Andreas Seeger===
+
===Matthew Schrecker===
  
Title: Singular integrals and a problem on mixing flows
+
Title: Finite energy methods for the 1D isentropic Euler equations
  
Abstract: The talk will be about  results related to Bressan's mixing problem. We present  an inequality for the change of a  Bianchini semi-norm of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator  for which one proves bounds  on Hardy spaces. This is joint work with Mahir Hadžić, Charles Smart and    Brian Street.
+
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.
  
===Sam Krupa===
+
===Lei Wu===
  
Title: Proving Uniqueness of Solutions for Burgers Equation Entropic for a Single Entropy, with Eye Towards Systems Case
+
Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects
  
Abstract: For hyperbolic systems of conservation laws, uniqueness of solutions is still largely open. We aim to expand the theory of uniqueness for systems of conservation laws. One difficulty is that many systems have only one entropy. This contrasts with scalar conservation laws, where many entropies exist. It took until 1994 to show that one entropy is enough to ensure uniqueness of solutions for the scalar conservation laws (Panov). This single entropy result was proven again by De Lellis, Otto and Westdickenberg in 2004. These two proofs both rely on the special connection between Hamilton--Jacobi equations and scalar conservation laws in one space dimension. However, this special connection does not extend to systems. In our new work, we prove the single entropy result for scalar conservation laws without using Hamilton--Jacobi. Our proof lays out new techniques that are promising for showing uniqueness of solutions in the systems case. This is joint work with A. Vasseur.
+
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.

Latest revision as of 18:52, 19 September 2018

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 2019-Spring 2020

PDE GA Seminar Schedule Fall 2018-Spring 2019

date speaker title host(s)
August 31 (FRIDAY), Julian Lopez-Gomez (Complutense University of Madrid) The theorem of characterization of the Strong Maximum Principle Rabinowitz
September 10, Hiroyoshi Mitake (University of Tokyo) On approximation of time-fractional fully nonlinear equations Tran
September 12 and September 14, Gunther Uhlmann (UWash) TBA Li
September 17, Changyou Wang (Purdue) Some recent results on mathematical analysis of Ericksen-Leslie System Tran
Sep 28, Colloquium Gautam Iyer (CMU) Stirring and Mixing Thiffeault
October 1, Matthew Schrecker (UW) Finite energy methods for the 1D isentropic Euler equations Kim and Tran
October 8, Anna Mazzucato (PSU) TBA Li and Kim
October 15, Lei Wu (Lehigh) Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects Kim
October 22, Annalaura Stingo (UCD) TBA Mihaela Ifrim
October 29, Yeon-Eung Kim (UW) TBA Kim and Tran
November 5, Albert Ai (UC Berkeley) TBA Mihaela Ifrim
December 3, Trevor Leslie (UW) TBA Kim and Tran
December 10, ( ) TBA
January 28, ( ) TBA
Time: TBD, Jessica Lin (McGill University) TBA Tran
March 4 Vladimir Sverak (Minnesota) TBA(Wasow lecture) Kim
March 18, Spring recess (Mar 16-24, 2019)
April 29, ( ) TBA

Abstracts

Julian Lopez-Gomez

Title: The theorem of characterization of the Strong Maximum Principle

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.

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.)


Changyou Wang

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

Title: Finite energy methods for the 1D isentropic Euler equations

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.

Lei Wu

Title: Hydrodynamic Limits in Kinetic Equations with Boundary Layer Effects

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.