Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

Eugen Varvarucaa1 p1

a1 Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK

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.

(Received May 08 2007)

(Accepted November 08 2007)

Correspondence:

p1 Present address: Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ (e.varvaruca@imperial.ac.uk).