The Cauchy problem for the nonisentropic compressible MHD fluids: Optimal time-decay rates

This paper is concerned with the time-decay rates of the strong solutions of the three-dimensional nonisentropic compressible magnetohydrodynamic (MHD) system. First, motivated by Pu and Guo's result [Z. Angew. Math. Phys. 64 (2013) 519-538], we establish the existence result of a unique local-in-time strong solution for the MHD system. Then, we derive a priori estimates and use the continuity argument to obtain the global-in-time solution, where the initial perturbation is small in H-2-norm. Finally, based on Fourier theory and the idea of cancelation of a low-medium frequent part as in [Sci. China Math. 65 (2022) 1199-1228], we get the optimal time-decay rates (including highest-order derivatives) of strong solutions for nonisentropic MHD fluids when the boundedness of L-1-norm of the initial perturbation is required. Our result is the first one concerning with the optimal decay estimates of the highest-order derivatives of the nonisentropic MHD system.