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

Author: Peter J. Olver
Journal: Trans. Amer. Math. Soc. 277 (1983), 353-380
MSC: Primary 35R35; Secondary 35L65, 35Q20, 76B15
MathSciNet review: 690057
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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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Keywords: Free boundary problem, conservation law, water waves, completely integrable, harmonic function
Article copyright: © Copyright 1983 American Mathematical Society