Dia: Dimecres, 20 de febrer de 2019
Lloc: Aula S01, Facultat de Matemàtiques i Estadística, UPC.
A càrrec de: Roberto Feola, University of Nantes
Títol: Birkhoff Normal Form and long time existence for periodic gravity water waves
Resum: We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth, and prove a rigorous reduction of these equations to Birkhoff normal form up to degree four. This prove a conjecture of Zakharov-Dyachenko based on the formal Birkhoff integrability of the waver waves Hamiltonian truncated at order four. As a consequence, we also obtain a long-time stability result: periodic perturbations of a flat interface that are of size ε in a sufficiently smooth Sobolev space lead to solutions that remain regular and small up to times of order ε−3
Last updated: Mon Feb 18 08:33:27 2019