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In this paper, we study the large time behavior of solutions to thecompressible magnetohydrodynamic equations in the $L^p$-type critical Besovspaces. Precisely, we show that if the initial data in the low frequenciesadditionally belong to some Besov space $\dot{B}_{2,\infty}^{-\sigma_1}$ with$\sigma_1\in (1-N/2, 2N/p-N/2]$, then the $\dot{B}_{p,1}^0$ norm of thecritical global solutions presents the optimal decay$t^{-\frac{N}{2}(\frac{1}{2}-\frac{1}{p})-\frac{\sigma_1}{2}}$ for$t\rightarrow+\infty$. The pure energy argument without the spectral analysisis performed, which allows us to remove the usual smallness assumption of lowfrequencies.

Optimal decay for the compressible MHD equations in the critical regularity framework