Global regularity for water waves in two dimensions

Job Candidate Talk
Thursday, December 12, 2013 - 11:05
1 hour (actually 50 minutes)
Skiles 005
Princeton University
We will start by describing some general features of quasilinear dispersive and wave equations. In particular we will discuss a few important aspects related to the question of global regularity for such equations. We will then consider the water waves system for the evolution of a perfect fluid with a free boundary. In 2 spatial dimensions, under the influence of gravity, we prove the existence of global irrotational solutions for suitably small and regular initial data. We also prove that the asymptotic behavior of solutions as time goes to infinity is different from linear, unlike the 3 dimensional case.