Mathematics Colloquium

Speaker: 
Albert Ai
Topic: 
Low regularity solutions for quasilinear PDEs

Abstract:

In this talk, we will consider the low regularity well-posedness problem for a pair of quasilinear dispersive PDEs: the nonlinear wave equation, and the water waves equations. Two classical methods, energy estimates and Strichartz estimates, have historically yielded substantial but partial results toward advancing the low regularity theory. We will see how, using a special structure of the equations known as a normal form structure, combined with tools from harmonic and microlocal analysis, we can refine these classical methods to substantially improve the known results for low regularity well-posedness.

Event Date: 
November 29, 2023 - 3:30pm
Location: 
110 MLH
Calendar Category: 
Colloquium