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Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

Published online by Cambridge University Press:  12 November 2008

Eugen Varvaruca
Eugen Varvaruca
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
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Abstract

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 6 , December 2008 , pp. 1345 - 1362
Copyright
Copyright © Royal Society of Edinburgh 2008

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