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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.11112 |
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| _version_ | 1866911026732072960 |
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| author | Huang, Yupei Zhang, Chilin |
| author_facet | Huang, Yupei Zhang, Chilin |
| contents | Singular steady states are important objects in obtaining ill-posedness results for 2D incompressible Euler equations. In \cite{elgindi2022regular}, a family of singular steady states near the Bahouri-Chemin patch was introduced. In this paper, we obtain the optimal convergence results for the singular steady states constructed in \cite{elgindi2022regular} to the Bahouri-Chemin patch. We first derive a boundary Harnack principle, and then obtain the optimal convergence results using the singular integral representation based on Green's function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11112 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal H{ö}lder convergence of a class of singular steady states to the Bahouri-Chemin patch Huang, Yupei Zhang, Chilin Analysis of PDEs Singular steady states are important objects in obtaining ill-posedness results for 2D incompressible Euler equations. In \cite{elgindi2022regular}, a family of singular steady states near the Bahouri-Chemin patch was introduced. In this paper, we obtain the optimal convergence results for the singular steady states constructed in \cite{elgindi2022regular} to the Bahouri-Chemin patch. We first derive a boundary Harnack principle, and then obtain the optimal convergence results using the singular integral representation based on Green's function. |
| title | Optimal H{ö}lder convergence of a class of singular steady states to the Bahouri-Chemin patch |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.11112 |