PDE Geometric Analysis seminar

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

PDE GA Seminar Schedule Fall 2017

date	speaker	title	host(s)
September 11	Mihaela Ifrim (UW)	Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation	Kim & Tran
September 18	Longjie Zhang (University of Tokyo)	TBD	Angenent
September 22, VV B239 4:00pm	Jaeyoung Byeon (KAIST)	Colloquium: Patterns formation for elliptic systems with large interaction forces	Rabinowitz
September 25	Tuoc Phan (UTK)	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)	Joint Analysis/PDE seminar	Tran
September 29, VV901 2:25pm	Dongnam Ko (CMU & SNU)	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)	TBD	Kim
October 16	Jingrui Cheng (UW)	TBD	Kim & Tran
October 23	Donghyun Lee (UW)	TBD	Kim & Tran
October 30	Myoungjean Bae (POSTECH)	TBD	Feldman
November 6	Jingchen Hu (USTC and UW)	TBD	Kim & Tran

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.

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.