The water waves equations: from Zakharov to Euler

Thomas Alazard (1) , Nicolas Burq (2) , Claude Zuily (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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 $C^1$.

Domaines: Equations aux dérivées partielles [math.AP]

Thomas Alazard, Nicolas Burq, Claude Zuily. The water waves equations: from Zakharov to Euler. 2012. ⟨hal-00760454⟩