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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2402.06364 |
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| _version_ | 1866910324215513088 |
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| author | Montalto, Riccardo Murgante, Federico Scrobogna, Stefano |
| author_facet | Montalto, Riccardo Murgante, Federico Scrobogna, Stefano |
| contents | In this paper we consider the generalized surface quasi-geostrophic $α$-SQG equations, in the "sublinear regime" $α\in (0, 1)$ and we study the stability of vortex patches close to vortex discs. We shall prove that for regular, Sobolev initial vortex patches $\varepsilon$-close to a vortex disc, the solutions stay $\varepsilon$-close to a vortex disc for a time interval of order $O(\varepsilon^{- 2})$. The proof is based on a paradifferential Birkhoff normal form reduction, implemented in the case where the dispersion relation is sublinear. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadratic lifespan for the sublinear $α$-SQG sharp front problem Montalto, Riccardo Murgante, Federico Scrobogna, Stefano Analysis of PDEs In this paper we consider the generalized surface quasi-geostrophic $α$-SQG equations, in the "sublinear regime" $α\in (0, 1)$ and we study the stability of vortex patches close to vortex discs. We shall prove that for regular, Sobolev initial vortex patches $\varepsilon$-close to a vortex disc, the solutions stay $\varepsilon$-close to a vortex disc for a time interval of order $O(\varepsilon^{- 2})$. The proof is based on a paradifferential Birkhoff normal form reduction, implemented in the case where the dispersion relation is sublinear. |
| title | Quadratic lifespan for the sublinear $α$-SQG sharp front problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.06364 |