Long-time behavior of solution to the compressible magnetohydrodynamic equations

In this paper, we study the long-time behavior of solution for the compressible magnetohydrodynamic equations in three-dimensional whole space. More precisely, we establish optimal decay rate for the higher-order spatial derivatives of solution, which improves the work of Li and Yu (2011), Chen and Tan (2010). Furthermore, one also investigates the long-time behavior for the mixed space–time derivatives of solution.