This summer school will be focused on the long term behavior and singularity formation for nonlinear PDEs arising from mathematical physics. It will consist of
three 3-hour mini-courses, and
several short contributed talks (lightning talks) by selected participants.
This summer school is organized by Sung-Jin Oh (UC Berkeley). Support is provided by UC Berkeley and by the National Science Foundation.
Contact:
Please contact Sung-Jin Oh for any questions about the summer school.
Sung-Jin Oh: Long time behavior of waves on asymptotically flat spacetimes: Uniform decay and late time tail.
Abstract: The goal of this lecture series is to give a coherent exposition of classical and recent techniques for studying the late time behavior of solutions to wave equations, which are possibly highly nonlinear, on asymptotically flat spacetime.
Federico Pasqualotto: Topics in incompressible fluids: instabilities and singularity formation
Abstract: In the course of these lectures, we will present three instances in which physical instabilities in
fluids generate small-scale effects of different nature.
Kihyun Kim: On long time dynamics for the self-dual Chern-Simons-Schrödinger equation within equivariant symmetry: rigidity of blow-up and rotational instability
Abstract: In this lecture series, we will consider the classification of long time dynamics of solutions, to so called self-dual Chern–Simons–Schrödinger equation (CSS), un- der equivariant symmetry (a variant of radial symmetry, roughly speaking). This equation was introduced by the physicists Jackiw and Pi in the 90s [1], as a gauged (or covariant) 2D cubic nonlinear Schrödinger equation (NLS) with an additional structure called self-duality. Although it looks more complicated than (NLS) at first glance, this geometric nonlinear Schrödinger equation turns out to have a surprisingly rigid long time dynamics (at least within equivariant symmetry): (i) soliton resolution, (ii) rigidity of finite-time blow-up, and (iii) rotational instability. We will explore this rigid dynamics using modulation analysis.