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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.02728 |
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| _version_ | 1866909456664625152 |
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| author | Cobb, Dimitri Donati, Martin Godard-Cadillac, Ludovic |
| author_facet | Cobb, Dimitri Donati, Martin Godard-Cadillac, Ludovic |
| contents | This article studies the vortex-wave system for the Surface Quasi-Geostrophic equation with parameter 0 < s < 1. We obtained local existence of classical solutions in H^4 under the standard ''plateau hypothesis'', H^2-stability of the solutions, and a blow-up criterion. In the sub-critical case s > 1/2 we established global existence of weak solutions. For the critical case s = 1/2, we introduced a weaker notion of solution (V-weak solutions) to give a meaning to the equation and prove global existence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex Cobb, Dimitri Donati, Martin Godard-Cadillac, Ludovic Analysis of PDEs This article studies the vortex-wave system for the Surface Quasi-Geostrophic equation with parameter 0 < s < 1. We obtained local existence of classical solutions in H^4 under the standard ''plateau hypothesis'', H^2-stability of the solutions, and a blow-up criterion. In the sub-critical case s > 1/2 we established global existence of weak solutions. For the critical case s = 1/2, we introduced a weaker notion of solution (V-weak solutions) to give a meaning to the equation and prove global existence. |
| title | Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.02728 |