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arXiv · 2602.22767

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

Marc Magaña·Joan Mateu·Joan Orobitg
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Abstract

We prove the persistence of boundary smoothness of vortex patches for the quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations generalize the Euler equations by including an additional parameter, the Rossby radius $\varepsilon^{-1}$, which modifies the relationship between the streamfunction and the (potential) vorticity. In addition, we prove that solutions of the QGSW equations converge locally in time to the corresponding Euler solutions as $\varepsilon \to 0$ in little H\"older spaces.

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Marc Magaña, Joan Mateu, Joan Orobitg. 2026-02-26. The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations. https://arxiv.org/abs/2602.22767

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