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.

Analyticity of periodic traveling free surface water waves with vorticity — University of
Vienna … Analyticity of periodic traveling free surface water waves with vorticity …