On time-decay rates of strong solutions for the 3D magnetohydrodynamics equations with nonlinear damping

In this paper we investigate the existence and time-decay rates of strong solutions with small perturbation to the systems of equations of a compressible magneto-hydrodynamic fluid with nonlinear damping. First we reformulate the system into a perturbation form. Then we establish a priori estimates of solutions, and prove the existence of the global-in-time based on the local existence of unique solutions. Finally we will establish the optimal time-decay rates of the non-homogeneous system by constructing some decay estimates of the linearized system based on the decomposition technique of both the low and high frequencies of solutions as in [40]. (C) 2022 Elsevier Inc. All rights reserved.