A Riemann-Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
type: Item
instance of: scholarly article
title: A Riemann-Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
zbMATH Open document ID: 1045.35113
DOI: 10.1016/S0294-1449(02)00006-9
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2003-04-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78573
review text: A Stokes wave is a steady periodic wave propagating under gravity with constant speed on the surface of an infinitely deep irrotational flow. The authors study the critical points of a certain functional in order to describe a Stokes wave, the free surface of which is characterized by the Bernoulli boundary condition. A number of properties of the solution of the associated Euler-Lagrange equation is established. Although the question as to whether for all critical points the true Bernoulli condition holds remains open, the authors show that the Bernoulli condition is always satisfied in a certain generalized sense.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 42A50
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 76M30
zbMATH DE Number: 1901026
zbMATH Keywords: regularity theory
zbMATH Keywords: Stokes waves
zbMATH Keywords: critical point
zbMATH Keywords: Bernoulli boundary condition
zbMATH Keywords: Euler-Lagrange equation
author: Eugene Shargorodsky
author: John F. Toland
reviewed by: Dmitry Shepelsky
MaRDI profile type: Publication
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OpenAlex ID: W2023782671
description: scientific article; zbMATH DE number 1901026