Asymptotic stability of stationary solutions for Hall magnetohydrodynamic equations

In this paper, we consider the large time behavior of the compressible Hall magnetohydrodynamic equations with Coulomb force in $R^3$ near the non-constant equilibrium state. We derive the global existence provided that the initial perturbation is sufficiently small. Moreover, under the further assumption that the doping profile is of small variation, we obtain the convergence rates by combining the linear $L^p$–$L^q$ decay estimates.