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

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 $u\in BM{O}^{-1}({\mathbb{R}}^3)$, 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.

References in corpus (3)

• On Liouville-type theorems for the 2D stationary MHD equations
• Liouville-type theorems for the planer stationary MHD equations with growth at infinity
• On Liouville type theorems for the stationary MHD and Hall-MHD systems