On Liouville-type theorems for the stationary MHD and the Hall-MHD systems in R3

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 Chae and Wolf (J Differ Equ 295:233–248, 2021). To prove our main theorems, we use a refined iteration argument. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.