Global Solutions for the Gravity Water Waves Equation in Dimension 3
Analysis of PDEs
2009-06-30 v1
Abstract
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L^2 related norms, with dispersive estimates, which give decay in L^\infty. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
Keywords
Cite
@article{arxiv.0906.5343,
title = {Global Solutions for the Gravity Water Waves Equation in Dimension 3},
author = {P. Germain and N. Masmoudi and J. Shatah},
journal= {arXiv preprint arXiv:0906.5343},
year = {2009}
}