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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.15040 |
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| _version_ | 1866912130598436864 |
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| author | Akridge, Zachary Bradshaw, Zachary |
| author_facet | Akridge, Zachary Bradshaw, Zachary |
| contents | The problem of regularity and uniqueness are open for the supercritically dissipative surface quasi-geostrophic equations in certain classes. In this note we examine the extent to which small or large scales are necessarily active both for the temperature in a hypothetical blow-up scenario and for the error in hypothetical non-uniqueness scenarios, the latter understood within the class of Marchand's solutions. This extends prior work for the 3D Navier-Stokes equations. The extension is complicated by the fact that mild solution techniques are unavailable for supercritical SQG. This forces us to develop a new approach using energy methods and Littlewood-Paley theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15040 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity, uniqueness and the relative size of small and large scales in SQG flows Akridge, Zachary Bradshaw, Zachary Analysis of PDEs 35Q35 The problem of regularity and uniqueness are open for the supercritically dissipative surface quasi-geostrophic equations in certain classes. In this note we examine the extent to which small or large scales are necessarily active both for the temperature in a hypothetical blow-up scenario and for the error in hypothetical non-uniqueness scenarios, the latter understood within the class of Marchand's solutions. This extends prior work for the 3D Navier-Stokes equations. The extension is complicated by the fact that mild solution techniques are unavailable for supercritical SQG. This forces us to develop a new approach using energy methods and Littlewood-Paley theory. |
| title | Regularity, uniqueness and the relative size of small and large scales in SQG flows |
| topic | Analysis of PDEs 35Q35 |
| url | https://arxiv.org/abs/2411.15040 |