Conservation Laws of Free Boundary Problems and the Classification of Conservation Laws for Water Waves
- 1 May 1983
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 277 (1) , 353-380
- https://doi.org/10.2307/1999361
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.Keywords
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