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The Water-Wave Equations: From Zakharov to Euler
Studies in Phase Space Analysis with Applications to PDEs
Starting form the Zakharov/Craig-Sulem formulation of the gravity 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 . L ∞ (I,H s+ 1 2 (R d ))doi:10.1007/978-1-4614-6348-1_1 fatcat:qgx5xkdcwfe4tgzfmmscyzees4