Difference between revisions of "PDE Geometric Analysis seminar"

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(PDE GA Seminar Schedule Fall 2017)
(PDE GA Seminar Schedule Fall 2018-Spring 2019)
 
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===[[Previous PDE/GA seminars]]===
 
===[[Previous PDE/GA seminars]]===
===[[Spring 2018 | Tentative schedule for Spring 2018]]===
+
===[[Fall 2019-Spring 2020 | Tentative schedule for Fall 2019-Spring 2020]]===
 +
 
 +
== PDE GA Seminar Schedule Fall 2018-Spring 2019 ==
 +
 
  
== PDE GA Seminar Schedule Fall 2017 ==
 
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!style="width:20%" align="left" | date   
 
!style="width:20%" align="left" | date   
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!align="left" | title
 
!align="left" | title
 
!style="width:20%" align="left" | host(s)
 
!style="width:20%" align="left" | host(s)
|-
+
 
|September 11
+
 
|Mihaela Ifrim (UW)
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|-  
|[[#Mihaela Ifrim| Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation]]
+
|September 10,
| Kim & Tran
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| Hiroyoshi Mitake (University of Tokyo)
|-
+
|[[#Hiroyoshi Mitake | TBA ]]
|September 18
+
|Longjie Zhang (University of Tokyo)  
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|[[#Longjie Zhang | On curvature flow with driving force starting as singular initial curve in the plane]]
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|  Angenent
+
|-
+
|September 22,
+
VV 9th floor hall, 4:00pm
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|Jaeyoung Byeon (KAIST)
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|[[#Jaeyoung Byeon|  Colloquium: Patterns formation for elliptic systems with large interaction forces]]
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|  Rabinowitz
+
|-
+
|September 25
+
| Tuoc Phan (UTK)
+
|[[#Tuoc Phan |  Calderon-Zygmund regularity estimates for weak solutions of quasi-linear parabolic equations with an application]]
+
 
| Tran
 
| Tran
|-  
+
|-
|September 26,  
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|September 17,
VV B139 4:00pm
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| Changyou Wang (Purdue)
| Hiroyoshi Mitake (Hiroshima University)
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|[[#Changyou Wang TBA ]]
|[[#Hiroyoshi Mitake Joint Analysis/PDE seminar: Derivation of multi-layered interface system and its application]]
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| Tran
 
| Tran
 +
|- 
 +
|September 24/26,
 +
| Gunther Uhlmann (UWash)
 +
|[[#Gunther Uhlmann | TBA ]]
 +
| Li
 +
|- 
 +
|October 1,
 +
| Matthew Schrecker (UW)
 +
|[[#Matthew Schrecker | TBA ]]
 +
| Kim and Tran
 +
|- 
 +
|October 8,
 +
| Anna Mazzucato (PSU)
 +
|[[#Anna Mazzucato | TBA ]]
 +
| Li and Kim
 +
|- 
 +
|October 15,
 +
| Lei Wu (Lehigh)
 +
|[[#Lei Wu | TBA ]]
 +
| Kim
 +
|- 
 +
|October 22,
 +
| Annalaura Stingo (UCD)
 +
|[[#Annalaura Stingo | TBA ]]
 +
| Mihaela Ifrim
 +
|- 
 +
|October 29,
 +
| Jessica Lin (McGill University)
 +
|[[#Jessica Lin | TBA ]]
 +
| Tran
 +
|- 
 +
|November 5,
 +
| Albert Ai (University of Berkeley)
 +
|[[#Albert Ai | TBA ]]
 +
| Mihaela Ifrim
 +
|- 
 +
|December 10,
 +
|  ( )
 +
|[[#  | TBA ]]
 +
 
|-  
 
|-  
|September 29,
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|January 28,
VV901 2:25pm
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|   ( )
| Dongnam Ko (CMU & SNU)
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|[[# | TBA ]]
|[[#Dongnam Ko | a joint seminar with ACMS: On the emergence of local flocking phenomena in Cucker-Smale ensembles ]]
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|
| Shi Jin & Kim
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|-
|-  
+
|March 4
|October 2
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| Vladimir Sverak (Minnesota)
| No seminar due to a KI-Net conference
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|[[#Vladimir Sverak | TBA(Wasow lecture) ]]
|
+
|
+
|-
+
|October 9
+
| Sameer Iyer (Brown University)
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|[[#Sameer Iyer | Global-in-x Steady Prandtl Expansion over a Moving Boundary ]]
+
 
| Kim
 
| Kim
|-  
+
|-
|October 16
+
|March 18,
| Jingrui Cheng (UW)
+
| Spring recess (Mar 16-24, 2019)
|[[#Jingrui Cheng |  A 1-D semigeostrophic model with moist convection ]]
+
|[[#  |  ]]
| Kim & Tran
+
|   
|-
+
|-
|October 23
+
|April 29,
| Donghyun Lee (UW)
+
|   ( )
|[[#Donghyun Lee | The Vlasov-Poisson-Boltzmann system in bounded domains ]]
+
|[[#  | TBA ]]
| Kim & Tran
+
|   
|-
+
|October 30
+
| Myoungjean Bae (POSTECH)
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|[[#Myoungjean Bae 3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system ]]
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Feldman
+
|-  
+
|November 6
+
| Jingchen Hu (USTC and UW)
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|[[#Jingchen Hu | Shock Reflection and Diffraction Problem with Potential Flow Equation ]]
+
| Kim & Tran
+
|-
+
|November 27
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| Ru-Yu Lai (Minnesota)
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|[[#Ru-Yu Lai |  TBD ]]
+
| Li
+
|-
+
|December 4
+
| Norbert Pozar (Kanazawa University)
+
|[[#Norbert Pozar TBD ]]
+
| Tran
+
 
|}
 
|}
  
==Abstracts==
+
== Abstracts ==
 
+
===Mihaela Ifrim===
+
 
+
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.
+
 
+
===Longjie Zhang===
+
 
+
On curvature flow with driving force starting as singular initial curve in the plane
+
 
+
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
+
 
+
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.
+
 
+
 
+
===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
+
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.
+
 
+
===Hiroyoshi Mitake===
+
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.
+
 
+
 
+
===Dongnam Ko===
+
On the emergence of local flocking phenomena in Cucker-Smale ensembles
+
 
+
Emergence of flocking groups are often observed in many complex network systems. The Cucker-Smale model is one of the flocking model, which describes the dynamics of attracting particles. This talk concerns time-asymptotic behaviors of Cucker-Smale particle ensembles, especially for mono-cluster and bi-cluster flockings. The emergence of flocking phenomena is determined by sufficient initial conditions, coupling strength, and communication weight decay. Our asymptotic analysis uses the Lyapunov functional approach and a Lagrangian formulation of the coupled system. We derive a system of differential inequalities for the functionals that measure the local fluctuations and group separations along particle trajectories. The bootstrapping argument is the key idea to prove the gathering and separating behaviors of Cucker-Smale particles simultaneously.
+
 
+
===Sameer Iyer===
+
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.
+
 
+
===Jingrui Cheng===
+
 
+
A 1-D semigeostrophic model with moist convection.
+
 
+
We consider a simplified 1-D model of semigeostrophic system with moisture, which describes moist convection in a single column in the atmosphere. In general, the solution is non-continuous and it is nontrivial part of the problem to find a suitable definition of weak solutions. We propose a plausible definition of such weak solutions which describes the evolution of the probability distribution of the physical quantities, so that the equations hold in the sense of almost everywhere. Such solutions are constructed from a discrete scheme which obeys the physical principles. This is joint work with Mike Cullen, together with Bin Cheng, John Norbury and Matthew Turner.
+
 
+
===Donghyun Lee===
+
 
+
We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition. Moreover we prove an exponential convergence of distribution function toward the global Maxwellian.
+
 
+
===Myoungjean Bae===
+
 
+
3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system.
+
 
+
I will present a recent result on the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler–Poisson system in a cylinder supplemented with non-small boundary data. A special Helmholtz decomposition of the velocity field is introduced for 3-D axisymmetric flow with a nonzero swirl (=angular momentum density) component.  This talk is based on a joint work with S. Weng (Wuhan University, China).
+
 
+
===Jingchen Hu===
+
  
Shock Reflection and Diffraction Problem with Potential Flow Equation
+
=== ===
  
In this talk, we will present our work on nonsymmetric shock reflection and diffraction problem, the equation concerned is potential flow equation, which is a simplification of Euler System, mainly based on the assumption that flow has no vortex. We showed in both nonsymmetric reflection case and diffraction case, that physically admissible solution does not exist. This implies that the formation of vortex is essential to maintain the structural stability of shock reflection and diffraction.
+
Title:

Latest revision as of 16:35, 14 August 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)


September 10, Hiroyoshi Mitake (University of Tokyo) TBA Tran
September 17, Changyou Wang (Purdue) TBA Tran
September 24/26, Gunther Uhlmann (UWash) TBA Li
October 1, Matthew Schrecker (UW) TBA Kim and Tran
October 8, Anna Mazzucato (PSU) TBA Li and Kim
October 15, Lei Wu (Lehigh) TBA Kim
October 22, Annalaura Stingo (UCD) TBA Mihaela Ifrim
October 29, Jessica Lin (McGill University) TBA Tran
November 5, Albert Ai (University of Berkeley) TBA Mihaela Ifrim
December 10, ( ) TBA
January 28, ( ) TBA
March 4 Vladimir Sverak (Minnesota) TBA(Wasow lecture) Kim
March 18, Spring recess (Mar 16-24, 2019)
April 29, ( ) TBA

Abstracts

Title: