Analyticity of periodic traveling free surface water waves with vorticity

Pages 559-568 from Volume 173 (2011), Issue 1 by Adrian Constantin, Joachim Escher

Abstract

We prove that the profile of a periodic traveling wave propagating at the surface of water above a flat bed in a flow with a real analytic vorticity must be real analytic, provided the wave speed exceeds the horizontal fluid velocity throughout the flow. The real analyticity of each streamline beneath the free surface holds even if the vorticity is only Hölder continuously differentiable.

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Keywords
, , ,
Mathematical Subject Classification
Primary: , , ,
DOI
http://doi.org/10.4007/annals.2011.173.1.12
MR
2753609
zbMATH
05960665
Milestones
Received: 20 February 2009
Revised: 11 November 2009
Accepted: 6 May 2010
Published online: 4 January 2011

Authors

Adrian Constantin

Faculty of Mathematics
University of Vienna
1089 Vienna
Austria

Joachim Escher

Institut für Angewandte Mathematik
Gottfried Wilhelm Leibniz Universität Hannover
30167 Hannover
Germany