New Liouville type theorems for the stationary MHD equations in $\mathbb{R}^3$

Abstract

We research the Liouville type problem for the 3D stationary MHD equations in the frequency space. We establish two new Liouville type theorems for solutions with finite Dirichlet energy. Specifically, we show that the low-frequency part of the velocity field plays the leading role in a Liouville theory for MHD equations and then improve the results of Chae-Weng \cite{Chae-W}.