Decay rate of strong solution for the compressible magnetohydrodynamic equations with large initial data

Abstract In this paper, we study the decay rate of strong solution for the compressible magnetohydrodynamics(MHD) equations with large initial data in three-dimensional whole space. First of all, it is shown that both the first and the second order spatial derivatives of magnetic field converge to zero at the same L 2 − rate ( 1 + t ) − 5 4 . Furthermore, we also prove that the lower bounds of decay rate for the magnetic field itself and first order spatial derivative at the L 2 − rate are ( 1 + t ) − 3 4 and ( 1 + t ) − 5 4 respectively.