Time quasi-periodic gravity water waves in finite depth

Analysis Seminar
Topic:Time quasi-periodic gravity water waves in finite depth
Speaker:Massimiliano Berti
Affiliation:International School for Advanced Studies
Date:Wednesday, November 8
Time/Room:2:30pm - 3:30pm/West Building Lecture Hall
Video Link:https://video.ias.edu/analysis/2017/1108-MassimilianoBerti

We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water waves solutions, namely periodic and even in the space variable $x$, of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a set of asymptotically full measure. This is a small divisor problem. The main difficulties are the fully nonlinear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity.