Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Fall 2017)
(PDE GA Seminar Schedule Fall 2020-Spring 2021)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Spring 2018 | Tentative schedule for Spring 2018]]===
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===[[Fall 2021-Spring 2022 | Tentative schedule for Fall 2021-Spring 2022]]===
  
== PDE GA Seminar Schedule Fall 2017 ==
 
{| cellpadding="8"
 
!style="width:20%" align="left" | date 
 
!align="left" | speaker
 
!align="left" | title
 
!style="width:20%" align="left" | host(s)
 
|-
 
|September 11
 
|Mihaela Ifrim (UW)
 
|[[#Mihaela Ifrim|  Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation]]
 
| Kim & Tran
 
|-
 
|September 18
 
|Longjie Zhang (University of Tokyo)
 
|[[#Longjie Zhang |  On curvature flow with driving force starting as singular initial curve in the plane]]
 
|  Angenent
 
|-
 
|September 22,
 
VV B239 4:00pm
 
|Jaeyoung Byeon (KAIST)
 
|[[#Jaeyoung Byeon|  Colloquium: Patterns formation for elliptic systems with large interaction forces]]
 
|  Rabinowitz
 
|-
 
|September 25
 
| Tuoc Phan (UTK)
 
|[[#Tuoc Phan |  Calderon-Zygmund regularity estimates for weak solutions of quasi-linear parabolic equations with an application]]
 
| Tran
 
|-
 
|September 26,
 
VV B139 4:00pm
 
| Hiroyoshi Mitake (Hiroshima University)
 
|[[#Hiroyoshi Mitake |  Joint Analysis/PDE seminar: Derivation of multi-layered interface system and its application]]
 
| Tran
 
|-
 
|September 29,
 
VV901 2:25pm
 
| Dongnam Ko (CMU & SNU)
 
|[[#Dongnam Ko |  a joint seminar with ACMS: TBD ]]
 
| Shi Jin & Kim
 
|-
 
|October 2
 
| No seminar due to a KI-Net conference
 
|
 
|
 
|-
 
|October 9
 
| Sameer Iyer (Brown University)
 
|[[#Sameer Iyer |  Global-in-x Steady Prandtl Expansion over a Moving Boundary ]]
 
| Kim
 
|-
 
|October 16
 
| Jingrui Cheng (UW)
 
|[[#Jingrui Cheng |  TBD ]]
 
| Kim & Tran
 
|-
 
|October 23
 
| Donghyun Lee (UW)
 
|[[#Donghyun Lee |  TBD ]]
 
| Kim & Tran
 
|-
 
|October 30
 
| Myoungjean Bae (POSTECH)
 
|[[#Myoungjean Bae |  TBD ]]
 
|  Feldman
 
|-
 
|November 6
 
| Jingchen Hu (USTC and UW)
 
|[[#Jingchen Hu |  TBD ]]
 
| Kim & Tran
 
|}
 
|-
 
|December 4
 
| Norbert Pozar (Kanazawa University)
 
|[[#Norbert Pozar |  TBD ]]
 
| Tran
 
|}
 
  
==Abstracts==
 
  
===Mihaela Ifrim===
+
== 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
 +
 
  
Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
 
  
Our goal is to take a first step toward understanding the long time dynamics of solutions for the Benjamin-Ono equation. While this problem is known to be both completely integrable and globally well-posed in $L^2$, much less seems to be known concerning its long time dynamics. We present that for small localized data the solutions have (nearly) dispersive dynamics almost globally in time. An additional objective is to revisit the $L^2$ theory for the Benjamin-Ono equation and provide a simpler, self-contained approach. This is joined work with Daniel Tataru.
+
'''Week 3 (9/13/2020-9/19/2020)'''
  
===Longjie Zhang===
+
1. Eugenia Malinnikova - Two questions of Landis and their applications. https://www.youtube.com/watch?v=lpTsW1noWTQ
  
On curvature flow with driving force starting as singular initial curve in the plane
+
2. Pierre Germain - On the derivation of the kinetic wave equation. https://youtu.be/ZbCjKwQ3KcE
  
We consider a family of axisymmetric curves evolving by its mean curvature with driving force in the plane. However, the initial curve is oriented singularly at origin. We investigate this problem by level set method and give some criteria to judge whether the interface evolution is fattening or not. In the end, we can classify the solutions into three categories and provide the asymptotic behavior in each category. Our main tools in this paper are level set method and intersection number principle.
 
  
===Jaeyoung Byeon===
 
  
Title: Patterns formation for elliptic systems with large interaction forces
+
'''Week 4 (9/20/2020-9/26/2020)'''
  
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions.   The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.
+
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
  
===Tuoc Phan===
 
Calderon-Zygmund regularity estimates for weak solutions of quasi-linear parabolic equations with an application.
 
  
Abstract: In this talk, we first introduce a problem on the existence of global time smooth solutions for a system of cross-diffusion equations. We then recall some classical results on regularity theories, and show that to solve our problem, new results on regularity theory estimates of Calderon-Zygmund type for gradients of solutions to a class of parabolic equations in Lebesgue spaces are required. We then discuss a result on Calderon-Zygmnud type estimate in the concrete setting to solve our
+
{| cellpadding="8"
mentioned problem regarding the system of cross-diffusion equations. The remaining part of the talk will be focused on some new generalized results on regularity gradient estimates for some general class of quasi-linear parabolic equations. Regularity estimates for gradients of solutions in Lorentz spaces will be presented. Ideas of the proofs for the results are given.
+
!style="width:20%" align="left" | date 
 +
!align="left" | speaker
 +
!align="left" | title
 +
!style="width:20%" align="left" | host(s)
 +
|-  
 +
|}
  
===Hiroyoshi Mitake===
+
== Abstracts ==
Derivation of multi-layered interface system and its application
 
  
Abstract: In this talk, I will propose a multi-layered interface system which can be formally derived by the singular limit of the weakly coupled system of the Allen-Cahn equation.  By using the level set approach, this system can be written as a quasi-monotone degenerate parabolic system. We give results of the well-posedness of viscosity solutions, and study the singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.
+
=== ===
  
===Iyer Sameer===
+
Title:
Title: Global-in-x Steady Prandtl Expansion over a Moving Boundary.
 
  
Abstract: I will outline the proof that steady, incompressible Navier-Stokes flows posed over the moving boundary, y = 0, can be decomposed into Euler and Prandtl flows globally in the tangential variable, assuming a sufficiently small velocity mismatch. The main obstacles in the analysis center around obtaining sharp decay rates for the linearized profiles and the remainders. The remainders are controlled via a high-order energy method, supplemented with appropriate embedding theorems, which I will present.
+
Abstract:

Latest revision as of 11:49, 20 September 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


date speaker title host(s)

Abstracts

Title:

Abstract: