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arXiv · 2101.12006

Pure gravity traveling quasi-periodic water waves with constant vorticity

Massimiliano Berti·Luca Franzoi·Alberto Maspero
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Abstract

We prove the existence of small amplitude time quasi-periodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a Nash-Moser implicit function iterative scheme we construct traveling nonlinear waves which pass through each other slightly deforming and retaining forever a quasiperiodic structure. These solutions exist for any fixed value of depth and gravity and restricting the vorticity parameter to a Borel set of asymptotically full Lebesgue measure.

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Massimiliano Berti, Luca Franzoi, Alberto Maspero. 2021-01-28. Pure gravity traveling quasi-periodic water waves with constant vorticity. https://arxiv.org/abs/2101.12006

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