Optimal decay rates of classical solutions for the full compressible MHD equations

In this paper, we are concerned with optimal decay rates for higher-order spatial derivatives of classical solutions to the full compressible MHD equations in three-dimensional whole space. If the initial perturbation is small in H3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H^3}$$\end{document}-norm and bounded in Lq(q∈1,65)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^q(q\in \left[1, \frac{6}{5} \right))}$$\end{document}-norm, we apply the Fourier splitting method by Schonbek (Arch Ration Mech Anal 88:209–222, 1985) to establish optimal decay rates for the second-order spatial derivatives of solutions and the third-order spatial derivatives of magnetic field in L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^2}$$\end{document}-norm. These results improve the work of Pu and Guo (Z Angew Math Phys 64:519–538, 2013).