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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.16128 |
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| _version_ | 1866918254591606784 |
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| author | Jeon, Junekey Zlatos, Andrej |
| author_facet | Jeon, Junekey Zlatos, Andrej |
| contents | We show that the generalized SQG equation on the plane is locally well-posed in spaces of low regularity solutions (essentially Hölder continuous with Hölder exponents depending on the equation parameter $α\in(0,\frac 12)$) that have $H^2$ level sets (i.e., with $L^2$ curvatures). Moreover, for $α\le\frac 16$ and initial data satisfying some additional hypotheses we show that the corresponding solutions can stop existing only when their level sets lose $H^2$-regularity, and hence not just due to level set collisions or "pile ups". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-Posedness for Low Regularity Solutions to the g-SQG Equation with Regular Level Sets Jeon, Junekey Zlatos, Andrej Analysis of PDEs We show that the generalized SQG equation on the plane is locally well-posed in spaces of low regularity solutions (essentially Hölder continuous with Hölder exponents depending on the equation parameter $α\in(0,\frac 12)$) that have $H^2$ level sets (i.e., with $L^2$ curvatures). Moreover, for $α\le\frac 16$ and initial data satisfying some additional hypotheses we show that the corresponding solutions can stop existing only when their level sets lose $H^2$-regularity, and hence not just due to level set collisions or "pile ups". |
| title | Well-Posedness for Low Regularity Solutions to the g-SQG Equation with Regular Level Sets |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.16128 |