Analyticity of rotational traveling capillary–gravity waves with critical layers

Abstract

We establish real analyticity of the free surface of a two-dimensional steady rotational flow of water with critical layers. The flow is acted upon by gravity and surface tension. We show that any Wloc2,∞-regular free surface is analytic provided the vorticity distribution is analytic. In particular, the surface of a water flow with constant vorticity is analytic.