Elliptic and Parabolic Equations - Abstract

Escher, Joachim

Analyticity of periodic travelling free surface water waves with vorticity

We prove that the profile of a travelling wave propagating at the surface with a flat bed in a flow with real analytic vorticity and without stagnation points must be real analytic. The real analyticity of each streamline beneath the free surface holds even if the vorticity is only Hölder continuously differentiable.