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arXiv · 2110.13751

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

Taoufik Hmidi·Emeric Roulley
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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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Taoufik Hmidi, Emeric Roulley. 2021-10-26. Time quasi-periodic vortex patches for quasi-geostrophic shallow-water equations. https://arxiv.org/abs/2110.13751

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