Analyticity of rotational water waves

Abstract

The aim of this survey is to review some recent results concerning the regularity properties of two-dimensional rotational free-surface flows. It is shown that for large classes of vorticity distributions, the corresponding free water surface together with all streamlines beneath are real-analytic curves. The models considered here include, besides classical periodic water waves of finite depth, solitary waves, waves with infinite depth, capillary waves, and waves over stratified flows. It is also pointed out that the analyticity of the streamlines leads to an intrinsic characterization of symmetric solitary waves with one single crest.