On Liouville type theorems for the stationary MHD and the Hall-MHD systems in $\mathbb{R}^3$

Abstract

In this paper we prove a Liouville type theorem for the stationary MHD and the stationary Hall-MHD systems. Assuming suitable growth condition at infinity for the mean oscillations for the potential functions, we show that the solutions are trivial. These results generalize the previous results obtained by two of the current authors in [6]. To prove our main theorems we use a refined iteration argument.