Some decay estimates of solutions for the 3-D compressible isentropic magnetohydrodynamics

Abstract

This paper is concerned with the time-asymptotic behavior of solutions to the threedimensional magnetohydrodynamics (MHD) for viscous compressible isentropic fluids. By exploiting some L p -L q estimates of solutions for the heat equation and the linearized Navier-Stokes system, the optimal decay estimates of the solution in L q with 2 q 6 and its first order derivative in L 2 are obtained when the initial perturbation around a constant state is sufficiently small in H 3 and is bounded in L p with any given 1 p < 6/5. As a byproduct, the global existence theorem is also proved.