The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910278320390144 |
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| author | Magaña, Marc Mateu, Joan Orobitg, Joan |
| author_facet | Magaña, Marc Mateu, Joan Orobitg, Joan |
| contents | 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 Hölder spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22767 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Magaña, Marc Mateu, Joan Orobitg, Joan Analysis of PDEs 35Q31, 35Q35 (Primary), 35B65, 35Q49, 35B30 (Secondary) 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 Hölder spaces. |
| title | The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations |
| topic | Analysis of PDEs 35Q31, 35Q35 (Primary), 35B65, 35Q49, 35B30 (Secondary) |
| url | https://arxiv.org/abs/2602.22767 |