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We revisit the 3D Cauchy problem of compressible heat-conductingmagnetohydrodynamic equations with vacuum as far field density. By delicateenergy method, we derive global existence and uniqueness of strong solutionsprovided that $(\|\rho_0\|_{L^\infty}+1)\big[\|\rho_0\|_{L^3}+\|\rho_0\|_{L^\infty}+1)^2\big(\|\sqrt{\rho_0}u_0\|_{L^2}^2+\|b_0\|_{L^2}^2\big)\big]\big[\|\nablau_0\|_{L^2}^2+(\|\rho_0\|_{L^\infty}+1)\big(\|\sqrt{\rho_0}E_0\|_{L^2}^2+\|\nablab_0\|_{L^2}^2\big)\big]$ is properly small. In particular, the smallnesscondition is independent of any norms of the initial data. This work improvesour previous results [18, 19].

Global strong solution for 3D compressible heat-conducting magnetohydrodynamic equations revisited