Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910452863205376 |
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| author | Han, Jingwen |
| author_facet | Han, Jingwen |
| contents | We show that any bounded smooth helically symmetric solution $(\Bu, \Bh)$ in $\mathbb{R}^3$ must be constant vectors. This is an extension of previous result \cite[Theorem 1.1]{HWXAHE} from Navier-Stokes system to MHD system. The proof relies on establishing a Saint-Venant type estimate to characterize the growth of Dirichlet integral of nontrivial solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$ Han, Jingwen Analysis of PDEs We show that any bounded smooth helically symmetric solution $(\Bu, \Bh)$ in $\mathbb{R}^3$ must be constant vectors. This is an extension of previous result \cite[Theorem 1.1]{HWXAHE} from Navier-Stokes system to MHD system. The proof relies on establishing a Saint-Venant type estimate to characterize the growth of Dirichlet integral of nontrivial solutions. |
| title | Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.11521 |