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arXiv · 2105.11667

Remarks on Liouville type theorems for the steady MHD and Hall-MHD equations

Xiaomeng Chen·Shuai Li·Wendong Wang
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Abstract

In this note we investigate Liouville type theorems for the steady three dimensional MHD and Hall-MHD equations, and show that the velocity field $u$ and the magnetic field $B$ are vanishing provided that $B\in L^{6,\infty}(\mathbb{R}^3)$ and $u\in BMO^{-1}(\mathbb{R}^3)$, which state that the velocity field plays an important role. Moreover, the similar result holds in the case of partial viscosity or diffusivity for the three dimensional MHD equations.

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Xiaomeng Chen, Shuai Li, Wendong Wang. 2021-05-25. Remarks on Liouville type theorems for the steady MHD and Hall-MHD equations. https://doi.org/10.1007/s00332-021-09768-4

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