Bifurcation of gravity-capillary Stokes waves with constant vorticity

TL;DR

This paper proves the existence of bifurcating periodic gravity-capillary water waves with constant vorticity for all parameter values, extending previous results and employing variational methods.

Contribution

It extends bifurcation results for gravity-capillary waves to all parameter values using variational techniques.

Findings

Bifurcation of periodic traveling water waves is proven for all parameter values.

Waves are parametrized by speed or momentum.

Results extend previous restricted-parameter bifurcation findings.

Abstract

We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves -- which are steady in a moving frame -- for {\it all} the values of gravity, surface tension, constant vorticity, depth and wavelenght, extending previous results valid for restricted values of the parameters. We parametrize the bifurcating Stokes waves either with their speed or their momentum.