Pure gravity traveling quasi-periodic water waves with constant vorticity

2021/01/28 by Massimiliano Berti, Berti, Massimiliano, Luca Franzoi +3 · 2 citations
Earth and Planetary Sciences · Mathematics · #(37K50 #35C07 #35S05) #37K55 #76B15 #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2101.12006

openalex publication_date 2021/01/28 · openalex created_date 2023/09/10 · openalex updated_date 2026/07/28

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.

Cited by

• Long time dynamics of space periodic water waves
• Two-dimensional water waves with constant vorticity and general bottom topography

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