Stability for the 3D generalized Hall‐MHD equations in the periodic domain

Abstract This paper studies stability of solutions for the 3D generalized incompressible Hall‐MHD Megnetohydrodynamics equations in the periodic domain with the magnetic field near a nontrivial equilibrium. Some new observations and estimates are implemented to exploit the enhanced dissipation produced by the nontrivial background magnetic field, which satisfies the Diophantine condition. Global stability and explicit time decay rates of solutions are shown.