Traveling quasi-periodic water waves with constant vorticity

Abstract

We prove the first bifurcation result of time quasi-periodic traveling waves solutions for space periodic water waves with vorticity. In particular we prove existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restricting the surface tension to a Borel set of asymptotically full Lebesgue measure.

arXiv comment87 pages

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• Time quasi-periodic vortex patches for quasi-geostrophic shallow-water equations
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• Three-layer water flows: Dirichlet-Neumann operators and approximations