Blow-up conditions for gravity water-waves
Analysis of PDEs
2014-07-28 v1
Abstract
We exhibit blow-up conditions for the gravity water-waves equations in any dimension and in domains with arbitrary bottoms. We follow the method by Alazard, Burq and Zuily of using a paradifferential reduction of the equations and derive precise a priori Sobolev estimates. Those estimates are then used to prove three different blow-up conditions where neither the boundedness of the curvature of the surface nor the boundedness in time of the Lipschitz norm of the velocity are needed.
Cite
@article{arxiv.1407.6881,
title = {Blow-up conditions for gravity water-waves},
author = {Thibault de Poyferré},
journal= {arXiv preprint arXiv:1407.6881},
year = {2014}
}