  This paper studies the Cauchy problem for three-dimensional viscous,
compressible, and heat conducting magnetohydrodynamic equations with vacuum as
far field density. We prove the global existence and uniqueness of strong
solutions provided that the quantity $\|\rho_0\|_{L^\infty}+\|b_0\|_{L^3}$ is
suitably small and the viscosity coefficients satisfy $3\mu>\lambda$. Here, the
initial velocity and initial temperature could be large. The assumption on the
initial density do not exclude that the initial density may vanish in a subset
of $\mathbb{R}^3$ and that it can be of a nontrivially compact support. Our
result is an extension of the works of Fan and Yu \cite{FY09} and Li et al.
\cite{LXZ13}, where the local strong solutions in three dimensions and the
global strong solutions for isentropic case were obtained, respectively. The
analysis is based on some new mathematical techniques and some new useful
energy estimates. This paper can be viewed as the first result concerning the
global existence of strong solutions with vacuum at infinity in some classes of
large data in higher dimension.
