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A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves

✍ Scribed by E. Shargorodsky; J.F. Toland

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
139 KB
Volume
20
Category
Article
ISSN
0294-1449

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✦ Synopsis

This paper concerns the question of equivalence between the Euler-Lagrange equation of a certain functional and periodic Stokes waves on the surface of an infinitely deep irrotational incompressible flow of an ideal fluid under gravity. Of particular concern is Bernoulli's constant-pressure condition on a free surface.

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## Abstract A body Ω floating in a fluid is subjected to small periodic displacement. Under idealized conditions the resulting wave pattern can be described by a linear boundary value problem for the Laplacian in an unbounded domain with a non‐coercive boundary condition on part of the boundary. Ne