A Rigorous Justification of the Modulation Approximation to the 2D Full Water Wave Problem
Analysis of PDEs
2015-05-20 v1
Abstract
We consider the 2D inviscid incompressible irrotational infinite depth water wave problem neglecting surface tension. Given wave packet initial data, we show that the modulation of the solution is a profile traveling at group velocity and governed by a focusing cubic nonlinear Schrodinger equation, with rigorous error estimates in Sobolev spaces. As a consequence, we establish existence of solutions of the water wave problem in Sobolev spaces for times in the NLS regime provided the initial data is suitably close to a wave packet of sufficiently small amplitude in Sobolev spaces.
Cite
@article{arxiv.1101.0545,
title = {A Rigorous Justification of the Modulation Approximation to the 2D Full Water Wave Problem},
author = {Nathan Totz and Sijue Wu},
journal= {arXiv preprint arXiv:1101.0545},
year = {2015}
}