Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917179940667392 |
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| author | Mengual, Francisco Solera, Marcos |
| author_facet | Mengual, Francisco Solera, Marcos |
| contents | We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique $\dot{H}^s$- energy solutions below the Miura-Ju class. In particular, this shows that the solutions constructed by Resnick and Marchand for the dissipative SQG equation are not necessarily unique. Second, this establishes nonuniqueness below the Ladyzhenskaya-Prodi-Serrin class for the 2D Navier-Stokes equation, as well as below the Constantin-Wu and Dong-Chen-Zhao-Liu classes for the dissipative SQG equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_00331 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations Mengual, Francisco Solera, Marcos Analysis of PDEs Mathematical Physics We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique $\dot{H}^s$- energy solutions below the Miura-Ju class. In particular, this shows that the solutions constructed by Resnick and Marchand for the dissipative SQG equation are not necessarily unique. Second, this establishes nonuniqueness below the Ladyzhenskaya-Prodi-Serrin class for the 2D Navier-Stokes equation, as well as below the Constantin-Wu and Dong-Chen-Zhao-Liu classes for the dissipative SQG equation. |
| title | Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2601.00331 |