On the well-posedness of the Hall-MHD system in a critical setting of Besov-Morrey type
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912089379962880 |
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| author | Ferreira, Lucas C. F. da Silva, Rafael P. |
| author_facet | Ferreira, Lucas C. F. da Silva, Rafael P. |
| contents | In this paper, we address the 3D incompressible Hall-magnetohydrodynamic system (Hall-MHD). Our objective is to provide local and global well-posedness results for initial velocity $u_{0}$, magnetic field $B_{0}$ and the current $J_{0}:=\nabla\times B_{0}$ in a new critical framework, namely critical Besov-Morrey spaces. These spaces combine typical characteristics from both Besov and Morrey spaces allowing a broader framework that encompasses the regularity properties inherent in Besov spaces with the Morrey space structure. Compared to previous works in Sobolev and Besov spaces, our approach accommodates a broader class of initial data, ensuring the construction of a unique solution over time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_20465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the well-posedness of the Hall-MHD system in a critical setting of Besov-Morrey type Ferreira, Lucas C. F. da Silva, Rafael P. Analysis of PDEs 35Q35, 76W05, 76D03, 42B35, 42B37 In this paper, we address the 3D incompressible Hall-magnetohydrodynamic system (Hall-MHD). Our objective is to provide local and global well-posedness results for initial velocity $u_{0}$, magnetic field $B_{0}$ and the current $J_{0}:=\nabla\times B_{0}$ in a new critical framework, namely critical Besov-Morrey spaces. These spaces combine typical characteristics from both Besov and Morrey spaces allowing a broader framework that encompasses the regularity properties inherent in Besov spaces with the Morrey space structure. Compared to previous works in Sobolev and Besov spaces, our approach accommodates a broader class of initial data, ensuring the construction of a unique solution over time. |
| title | On the well-posedness of the Hall-MHD system in a critical setting of Besov-Morrey type |
| topic | Analysis of PDEs 35Q35, 76W05, 76D03, 42B35, 42B37 |
| url | https://arxiv.org/abs/2410.20465 |