Conservation laws of free boundary problems and the classification of conservation laws for water waves

Olver, Peter J.

doi:10.1090/S0002-9947-1983-0690057-X

Conservation laws of free boundary problems and the classification of conservation laws for water waves
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Trans. Amer. Math. Soc. 277 (1983), 353-380 Request permission

Abstract:

The two-dimensional free boundary problem for incompressible irrotational water waves without surface tension is proved to have exactly eight nontrivial conservation laws. Included is a discussion of what constitutes a conservation law for a general free boundary problem, and a characterization of conservation laws for two-dimensional free boundary problems involving a harmonic potential proved using elementary methods from complex analysis.

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