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

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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 are small in $H^3$-norm and bounded in $L^q(q\in \left[1, \frac{6}{5}\right))$-norm, we apply the Fourier splitting method by Schonbek[Arch. Rational Mech. Anal. 88 (1985)] to establish optimal decay rates for the second order spatial derivatives of solutions and the third order spatial derivatives of magnetic field in $L^2$-norm. These results improve the work of Pu and Guo [Z. Angew. Math. Phys. 64 (2013) 519-538].