An Onsager-type theorem for SQG
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914857288204288 |
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| author | Dai, Mimi Giri, Vikram Radu, Razvan-Octavian |
| author_facet | Dai, Mimi Giri, Vikram Radu, Razvan-Octavian |
| contents | We construct non-trivial weak solutions $θ\in C_t^0C_x^{0-}$ to the surface quasi-geostrophic (SQG) equations, which have compact support in time and, thus, violate the conservation of the Hamiltonian. The result is sharp in view of the fact that such a conservation law holds for all weak solutions in the class $C_{t,x}^0 \subset L_{t,x}^3$ (Isett-Vicol, 2015) and resolves the Onsager conjecture for SQG. The construction is achieved by means of a Nash iteration together with the linear decoupling method recently introduced in Giri-Radu (2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Onsager-type theorem for SQG Dai, Mimi Giri, Vikram Radu, Razvan-Octavian Analysis of PDEs We construct non-trivial weak solutions $θ\in C_t^0C_x^{0-}$ to the surface quasi-geostrophic (SQG) equations, which have compact support in time and, thus, violate the conservation of the Hamiltonian. The result is sharp in view of the fact that such a conservation law holds for all weak solutions in the class $C_{t,x}^0 \subset L_{t,x}^3$ (Isett-Vicol, 2015) and resolves the Onsager conjecture for SQG. The construction is achieved by means of a Nash iteration together with the linear decoupling method recently introduced in Giri-Radu (2023). |
| title | An Onsager-type theorem for SQG |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.02582 |