Analyticity of periodic traveling free surface water waves with vorticity


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.


Adrian Constantin

Faculty of Mathematics
University of Vienna
1089 Vienna

Joachim Escher

Institut für Angewandte Mathematik
Gottfried Wilhelm Leibniz Universität Hannover
30167 Hannover