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

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

2007-08-31

arxiv.org/abs/0708.4371v1

Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 1345-1362

Mathematics

Complex Variables

Scientific paper

We study weak solutions for a class of free boundary problems which includes
as a special case the classical problem of traveling 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.

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