Wellposedness of inviscid SQG in the half-plane
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915331930324992 |
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| author | Jeong, In-Jee Kim, Junha Miura, Hideyuki |
| author_facet | Jeong, In-Jee Kim, Junha Miura, Hideyuki |
| contents | We consider the SQG equation without dissipation on the half-plane with Dirichlet boundary condition, and prove local wellposedness in the spaces $W^{3,p}$ and $C^{2,β}$ for any $1<p<\infty$ and $0<β<1$. We complement this wellposedness by showing that for generic $C^{\infty}_{0}$ initial data, the unique corresponding solution does not belong to $W^{3,\infty}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wellposedness of inviscid SQG in the half-plane Jeong, In-Jee Kim, Junha Miura, Hideyuki Analysis of PDEs We consider the SQG equation without dissipation on the half-plane with Dirichlet boundary condition, and prove local wellposedness in the spaces $W^{3,p}$ and $C^{2,β}$ for any $1<p<\infty$ and $0<β<1$. We complement this wellposedness by showing that for generic $C^{\infty}_{0}$ initial data, the unique corresponding solution does not belong to $W^{3,\infty}$. |
| title | Wellposedness of inviscid SQG in the half-plane |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.06601 |