Large time behavior of the compressible magnetohydrodynamic equations with Coulomb force

Abstract

In this paper, we consider the large time behavior of the solutions near a constant equilibrium state to the Cauchy problem for the compressible magnetohydrodynamic equations with Coulomb force in R3. Under the assumptions that the H3 norm of the initial data is small, but its higher order derivatives could be large, we obtain the optimal time decay rates of the solutions and their higher-order spatial derivatives by introducing the negative Sobolev and Besov spaces. As an immediate byproduct, the Lp–L2(1⩽p⩽2) type of the decay rates follows without requiring the smallness for Lp norm of initial data.