Global well-posedness of the MHD boundary layer equations in the Sobolev Space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866929505777483776 |
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| author | Li, Wei-Xi Xu, Zhan Yang, Anita |
| author_facet | Li, Wei-Xi Xu, Zhan Yang, Anita |
| contents | We study the two-dimensional MHD boundary layer equations. For small perturbation around a tangential background magnetic field, we obtain the global-in-time existence and uniqueness of solutions in Sobolev spaces. The proof relies on the novel combination of the well-explored cancellation mechanism and the idea of linearly-good unknowns, and we use the former idea to deal with the top tangential derivatives and the latter one admitting fast decay rate to control lower-order derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the MHD boundary layer equations in the Sobolev Space Li, Wei-Xi Xu, Zhan Yang, Anita Analysis of PDEs We study the two-dimensional MHD boundary layer equations. For small perturbation around a tangential background magnetic field, we obtain the global-in-time existence and uniqueness of solutions in Sobolev spaces. The proof relies on the novel combination of the well-explored cancellation mechanism and the idea of linearly-good unknowns, and we use the former idea to deal with the top tangential derivatives and the latter one admitting fast decay rate to control lower-order derivatives. |
| title | Global well-posedness of the MHD boundary layer equations in the Sobolev Space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.11009 |