Liouville type theorems for the stationary Hall-MHD equations in local Morrey spaces

Abstract

This paper is concerned with the Liouville type theorems for the 3D stationary incompressible Hall-MHD equations. We establish that under some sufficient conditions in local Morrey spaces, solutions of the stationary Hall-MHD equations are identically zero. In particular, we also prove Liouville type results for the stationary incompressible MHD equations on ${\mathbb{R}}^3$. Our theorems extend and generalize the classical results for the stationary incompressible Navier-Stokes equations.