Confinement results near point vortices on the rotating sphere
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917456056942592 |
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| author | Donati, Martin Roulley, Emeric |
| author_facet | Donati, Martin Roulley, Emeric |
| contents | We study the Euler equation on the rotating sphere in the case where the absolute vorticity is initially sharply concentrated around several points. We follow the literature already concerning vorticity confinement for the planar Euler equations, and obtain similar results on the rotating sphere, with new challenges due to the geometry. More precisely, we show the improbability of collisions for point-vortices, logarithmic in time absolute vorticity confinement for general configurations, the optimality of this last result in general, and the existence of configurations with power-law long confinement. We take this opportunity to write a unified, self-contained, and improved version of all the proofs, previously scattered across multiple papers on the planar case, with detailed exposition for pedagogical clarity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Confinement results near point vortices on the rotating sphere Donati, Martin Roulley, Emeric Analysis of PDEs Atmospheric and Oceanic Physics 76B47, 34A34, 37N10 We study the Euler equation on the rotating sphere in the case where the absolute vorticity is initially sharply concentrated around several points. We follow the literature already concerning vorticity confinement for the planar Euler equations, and obtain similar results on the rotating sphere, with new challenges due to the geometry. More precisely, we show the improbability of collisions for point-vortices, logarithmic in time absolute vorticity confinement for general configurations, the optimality of this last result in general, and the existence of configurations with power-law long confinement. We take this opportunity to write a unified, self-contained, and improved version of all the proofs, previously scattered across multiple papers on the planar case, with detailed exposition for pedagogical clarity. |
| title | Confinement results near point vortices on the rotating sphere |
| topic | Analysis of PDEs Atmospheric and Oceanic Physics 76B47, 34A34, 37N10 |
| url | https://arxiv.org/abs/2602.10061 |