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.

Pure gravity traveling quasi-periodic water waves with constant vorticity / Berti, M; Franzoi, L; Maspero, A. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - (2023), pp. 1-80. [10.1002/cpa.22143]

Pure gravity traveling quasi-periodic water waves with constant vorticity

Berti, M;Franzoi, L
;
Maspero, A
2023-01-01

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.
2023
1
80
https://onlinelibrary.wiley.com/doi/10.1002/cpa.22143?af=R
https://arxiv.org/abs/2101.12006
Berti, M; Franzoi, L; Maspero, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/134930
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