Liouville type theorems for the stationary Hall‐magnetohydrodynamic equations in local Morrey spaces

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