# 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.