Blow-up conditions for gravity water-waves

2014/07/25 by Thibault de Poyferré, de Poyferré, Thibault
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1407.6881

arxiv created 2014/07/25 · arxiv updated 2014/07/28

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.

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