English

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.

Keywords

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}
}
R2 v1 2026-06-22T05:13:11.676Z