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.

Traveling quasi-periodic water waves with constant vorticity / Berti, Massimiliano; Franzoi, Luca; Maspero, Alberto. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 1432-0673. - 240:1(2021), pp. 99-202. [10.1007/s00205-021-01607-w]

Traveling quasi-periodic water waves with constant vorticity

Massimiliano Berti;Luca Franzoi;Alberto Maspero
2021

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.
240
1
99
202
http://arxiv.org/abs/2004.08905v1
Berti, Massimiliano; Franzoi, Luca; Maspero, Alberto
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/117393
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