The Water-Wave Equations: From Zakharov to Euler

DOI10.1007/978-1-4614-6348-1_1zbMath1273.35220arXiv1212.0632OpenAlexW1660111745MaRDI QIDQ2848247

Nicolas Burq, Claude Zuily, Thomas Alazard

Publication date: 26 September 2013

Published in: Progress in Nonlinear Differential Equations and Their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.0632

zbMATH Keywords

Euler equationsCauchy theorywater-wave system

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Pseudodifferential operators as generalizations of partial differential operators (35S05) PDEs in connection with fluid mechanics (35Q35) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Continuation and prolongation of solutions to PDEs (35B60) Singular elliptic equations (35J75)

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Cites Work

• On the Cauchy problem for gravity water waves
• On the water-wave equations with surface tension
• Numerical simulation of gravity waves
• Well-posedness in Sobolev spaces of the full water wave problem in 2D
• Well-posedness of the water-waves equations
• Unnamed Item