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 language | English |
|---|---|
| Pages (from-to) | 901-917 |
| Number of pages | 17 |
| Journal | Journal des Mathematiques Pures et Appliquees |
| Volume | 79 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 9 Nov 2000 |
Funding
This work was supported by an EPSRC Senior Fellowship. I am grateful to my colleague Boris Buffoni for his interest.
Keywords
- Bernoulli problem
- Free-boundary problem
- Regularity theory
- Stokes waves
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics
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