Stokes waves in hardy spaces and as distributions

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17 Citations (Scopus)

Abstract

This paper deals with some functional-analytic questions which arise when the Stokeswave problem, for the free boundary of a steady irrotational water wave, is formulated as a quadratic equation for a 2π-periodic, real-valued function w on ℝ which need not be weakly differentiable. It is shown how any solution w of bounded variation which lies in the fractional order Sobolev space H1/2 must be real-analytic and describes the profile of a steady water wave. The investigation involves only elementary real and complex Hardy space theory.

Original languageEnglish
Pages (from-to)901-917
Number of pages17
JournalJournal des Mathematiques Pures et Appliquees
Volume79
Issue number9
DOIs
Publication statusPublished - 9 Nov 2000

Keywords

  • Bernoulli problem
  • Free-boundary problem
  • Regularity theory
  • Stokes waves

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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