Time quasi-periodic vortex patches for quasi-geostrophic shallow-water equations

2021/10/26 by Taoufik Hmidi, Hmidi, Taoufik, Emeric Roulley +1 · 1 citation
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #Quantum chaos and dynamical systems #math.AP #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.2110.13751

167 pages

arxiv created 2021/10/26 · openalex publication_date 2021/10/26 · arxiv updated 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we shall implement KAM theory in order to construct a large class of time quasi-periodic solutions for an active scalar model arising in fluid dynamics. More precisely, the construction of invariant tori is performed for quasi-geostrophic shallow-water equations when the \it Rossby deformation length belongs to a massive Cantor set. As a consequence, we construct pulsating vortex patches whose boundary is localized in a thin annulus for any time.

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• Boundary effects on the emergence of quasi-periodic solutions for Euler equations

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