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In this paper, the large-time behavior of solutions to the Cauchy problem for the 3D compressible MHD equations is considered with the effect of external force. We construct the global unique solution with the small initial data near the stationary profile. The optimal time decay rates of the solution to the system are built in multifrequency decompositions.

Optimal Convergence Rates for the Strong Solutions to the Compressible MHD Equations with Potential Force