Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$

Jingwen Han

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arXiv · 2405.11521

Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$

Jingwen Han

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Abstract

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.

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Jingwen Han. 2024-05-19. Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$. https://arxiv.org/abs/2405.11521

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