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

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arxiv 2110.13751 v1 pith:AJOWPD7M submitted 2021-10-26 math.AP physics.flu-dyn

Taoufik Hmidi , Emeric Roulley This is my paper · ORCID
classification math.APphysics.flu-dyn
keywords timeconstructequationspatchesquasi-geostrophicquasi-periodicshallow-watervortex
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Time Quasi-Periodic Three-dimensional Traveling Gravity Water Waves

    math.AP 2025-09 conditional novelty 8.0 of 10

    Existence of small-amplitude, linearly stable, time quasi-periodic traveling solutions for 3D pure gravity water waves in finite depth on tori, for generic lattices and most depths.

  2. Time-periodic vortices near translating symmetric dipole patches

    math.AP 2026-07 accept novelty 7.0 of 10

    Non-rigid time-periodic vortex patch solutions bifurcating from translating symmetric dipoles are constructed for the 2D Euler equations using Lyapunov-Schmidt reduction and Nash-Moser methods.

  3. On stationary Quasi-Geostrophic Shallow-Water flows

    math.AP 2026-07 accept novelty 7.0 of 10

    Non-trivial m-fold doubly-connected stationary vortex patches are proven to exist for the quasi-geostrophic shallow-water equations via bifurcation from annuli.

  4. The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations

    math.AP 2026-02 conditional novelty 4.0 of 10

    For the QGSW equations, a C^{1,γ} vortex patch boundary stays C^{1,γ} for all time, and as the inverse Rossby radius ε→0 the solutions converge to 2D Euler in little Hölder spaces on a uniform time interval.

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