Liouville type theorem for double Beltrami solutions of the Hall-MHD system in $\Bbb R^3$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910944624377856 |
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| author | Chae, Dongho |
| author_facet | Chae, Dongho |
| contents | In this paper we prove Liouville type theorem for the double Beltrami solutions to the stationary Hall-MHD equations in $\Bbb R^3$. Let $(u, B)$ be a smooth double Beltrami solution to the stationary Hall-MHD equations in $\Bbb R^3$, satisfying $\int_{\Bbb R^3} (|u|^q + |B|^q )dx <+\infty$ for some $q\in [2, 3)$, then $u=B=0$. In the case of $B=0$ the theorem reduces the previously known Liouville type result for the Beltrami solutions to the Euler equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Liouville type theorem for double Beltrami solutions of the Hall-MHD system in $\Bbb R^3$ Chae, Dongho Analysis of PDEs 35Q30, 76D05, 76D03 In this paper we prove Liouville type theorem for the double Beltrami solutions to the stationary Hall-MHD equations in $\Bbb R^3$. Let $(u, B)$ be a smooth double Beltrami solution to the stationary Hall-MHD equations in $\Bbb R^3$, satisfying $\int_{\Bbb R^3} (|u|^q + |B|^q )dx <+\infty$ for some $q\in [2, 3)$, then $u=B=0$. In the case of $B=0$ the theorem reduces the previously known Liouville type result for the Beltrami solutions to the Euler equations. |
| title | Liouville type theorem for double Beltrami solutions of the Hall-MHD system in $\Bbb R^3$ |
| topic | Analysis of PDEs 35Q30, 76D05, 76D03 |
| url | https://arxiv.org/abs/2505.00885 |