Horizontally periodic generalized surface quasigeostrophic patches and layers
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910917836406784 |
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| author | Ambrose, David M. Hadadifard, Fazel Kelliher, James P. |
| author_facet | Ambrose, David M. Hadadifard, Fazel Kelliher, James P. |
| contents | We study solutions to the $α$-SQG equations, which interpolate between the incompressible Euler and surface quasi-geostrophic equations. We extend prior results on existence of bounded patches, proving propagation of $H^k$-regularity of the patch boundary, $k \ge 3$, for finite time for patches that are periodic in one spatial dimension. Such periodic patches also encompass layers, or two-sided fronts. As the authors have treated the Euler case in prior work, we now primarily focus on the range of $α$ for which $α$-SQG lies strictly between the Euler and SQG equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Horizontally periodic generalized surface quasigeostrophic patches and layers Ambrose, David M. Hadadifard, Fazel Kelliher, James P. Analysis of PDEs 76B03 We study solutions to the $α$-SQG equations, which interpolate between the incompressible Euler and surface quasi-geostrophic equations. We extend prior results on existence of bounded patches, proving propagation of $H^k$-regularity of the patch boundary, $k \ge 3$, for finite time for patches that are periodic in one spatial dimension. Such periodic patches also encompass layers, or two-sided fronts. As the authors have treated the Euler case in prior work, we now primarily focus on the range of $α$ for which $α$-SQG lies strictly between the Euler and SQG equations. |
| title | Horizontally periodic generalized surface quasigeostrophic patches and layers |
| topic | Analysis of PDEs 76B03 |
| url | https://arxiv.org/abs/2504.17199 |