Strong illposedness for SQG in critical Sobolev spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866929241268944896 |
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| author | Jeong, In-Jee Kim, Junha |
| author_facet | Jeong, In-Jee Kim, Junha |
| contents | We prove that the inviscid surface quasi-geostrophic (SQG) equations are strongly ill-posed in critical Sobolev spaces: there exists an initial data $H^{2}(\bbT^2)$ without any solutions in $L^\infty_{t}H^{2}$. Moreover, we prove strong critical norm inflation for $C^\infty$--smooth data. Our proof is robust and extends to give similar ill-posedness results for the family of modified SQG equations which interpolate the SQG with two-dimensional incompressible Euler equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_07739 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Strong illposedness for SQG in critical Sobolev spaces Jeong, In-Jee Kim, Junha Analysis of PDEs We prove that the inviscid surface quasi-geostrophic (SQG) equations are strongly ill-posed in critical Sobolev spaces: there exists an initial data $H^{2}(\bbT^2)$ without any solutions in $L^\infty_{t}H^{2}$. Moreover, we prove strong critical norm inflation for $C^\infty$--smooth data. Our proof is robust and extends to give similar ill-posedness results for the family of modified SQG equations which interpolate the SQG with two-dimensional incompressible Euler equations. |
| title | Strong illposedness for SQG in critical Sobolev spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2107.07739 |