|Topic:||Time quasi-periodic gravity water waves in finite depth|
|Affiliation:||International School for Advanced Studies|
|Date:||Wednesday, November 8|
|Time/Room:||2:30pm - 3:30pm/West Building Lecture Hall|
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.