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.