The asymptotic behavior of globally smooth solutions to the compressible magnetohydrodynamic equations with Coulomb force

Abstract

The asymptotic stability of the steady state with the strictly positive constant density and the vanishing velocity and magnetic field to the Cauchy problem of the three-dimensional compressible viscous, heat-conducting magnetohydrodynamic equations with Coulomb force is established under small initial perturbations. Using a general energy method, we obtain the optimal time decay rates of the solution and its higher-order spatial derivatives by introducing the negative Sobolev and Besov spaces. As a corollary, the [Formula: see text]–[Formula: see text] [Formula: see text] type of the decay rates follows without requiring that the [Formula: see text] norm of initial data is small.