Regularity results for deep-water waves with Hölder continuous vorticity

Abstract

In this paper we study the regularity properties of periodic deep-water waves travelling under the influence of gravity. The flow beneath the wave surface is assumed to be rotational and the vorticity function is taken to be uniformly Hölder continuous. Excluding the presence of stagnation points, we transform the problem on a fixed reference half-plane and we use Schauder estimates to prove that the streamlines and the free surface of such waves are real-analytic graphs.

Keywords:

• deep-water waves
• real-analytic
• streamlines
• vorticity

AMS Subject Classifications::

• 35J25
• 76B03
• 76B47