Time Quasi-Periodic Traveling Gravity Water Waves in Infinite Depth
Analysis of PDEs
2020-11-26 v1
Abstract
We present the recent result [8] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the first existence result of quasi-periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash-Moser scheme, Birkhoff normal form methods and pseudo-differential calculus techniques. We deal with the combined problems of small divisors and the fully-nonlinear nature of the equations.
Keywords
Cite
@article{arxiv.2011.12794,
title = {Time Quasi-Periodic Traveling Gravity Water Waves in Infinite Depth},
author = {Roberto Feola and Filippo Giuliani},
journal= {arXiv preprint arXiv:2011.12794},
year = {2020}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2005.08280