Boundary regularity of uniformly rotating vortex patches and an unstable elliptic free boundary problem
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914514643976192 |
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| author | Wang, Yuchen Zhang, Guanghui Zhou, Maolin |
| author_facet | Wang, Yuchen Zhang, Guanghui Zhou, Maolin |
| contents | In this paper, we consider the sign-changing free boundary problem related to the uniformly rotating vortex patch solutions of the two-dimensional incompressible Euler equations. We prove that the boundary of the vortex patch locally forms a $90^\circ$ corner near singular boundary points, if the patch is Lipschitz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03498 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundary regularity of uniformly rotating vortex patches and an unstable elliptic free boundary problem Wang, Yuchen Zhang, Guanghui Zhou, Maolin Analysis of PDEs In this paper, we consider the sign-changing free boundary problem related to the uniformly rotating vortex patch solutions of the two-dimensional incompressible Euler equations. We prove that the boundary of the vortex patch locally forms a $90^\circ$ corner near singular boundary points, if the patch is Lipschitz. |
| title | Boundary regularity of uniformly rotating vortex patches and an unstable elliptic free boundary problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2306.03498 |