Decay of the compressible magnetohydrodynamic equations

Abstract

In this paper, we study the time decay rates of the solution to the Cauchy problem for the compressible heat-conducting magnetohydrodynamic equations via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. The $${\dot{H}^{-s}(0\leq s<\frac{3}{2})}$$ negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.