Zijin Li, Xinghong Pan
Published 2019-03-13Version 1
In this paper, we study the stationary magnetohydrodynamics system in $\mathbb{R}^2\times\mathbb{T}$. We prove trivialness of D-solutions (the velocity field $u$ and the magnetic field $h$) when they are swirl-free. Meanwhile, this Liouville type theorem also holds provided $u$ is swirl-free and $h$ is axially symmetric, or both $u$ and $h$ are axially symmetric. Our method is also valid for certain related boundary value problems in the slab $\mathbb{R}^2\times[-\pi,\,\pi]$.
On Liouville type theorem for the stationary magnetohydrodynamics system
Liouville type theorem for double Beltrami solutions of the Hall-MHD system in $\Bbb R^3$
On Liouville type theorems for the stationary MHD and the Hall-MHD systems in $\mathbb{R}^3$
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