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The water waves equations: from Zakharov to Euler

2012/12/04 by Thomas Alazard, Nicolas Burq, Alazard, Thomas +3
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Ocean Waves and Remote Sensing #math.AP

paper · pdf · doi:10.48550/arxiv.1212.0632

16 pages

arxiv created 2012/12/04 · openalex publication_date 2012/12/04 · arxiv updated 2012/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Starting form the Zakharov/Craig-Sulem formulation of the water-waves equations, we prove that one can define a pressure term and hence obtain a solution of the classical Euler equations. It is proved that these results hold in rough domains, under minimal assumptions on the regularity to ensure, in terms of Sobolev spaces, that the solutions are C1.

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