A note on the Liouville type theorem for the smooth solutions of the stationary Hall-MHD system

Abstract

The main result of this work is to study the Liouville type theorem for the stationary Hall-MHD system on $\mathbb{R}^{3}$. Specificaly, we show that if $(u,B)$ is a smooth solutions to Hall-MHD equations satisfying $(u,B) \in L^\frac{9}{2} \mathbb{R}^{3}$, then we have $u=B=0$. This improves a recent result of Chae et al. [2] and Zujin et al. [14].

Keywords

• Stationary Hall-MHD equations| Liouville type theorem