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 \(\Vert \rho _0\Vert _{L^\infty }+\Vert b_0\Vert _{L^3}\) 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 does 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 (Nonlinear Anal Real World Appl 10:392–409, 2009) and Li et al. (SIAM J Math Anal 45:1356–1387, 2013), 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.

本文研究了具有真空和远场密度的三维粘性，可压缩和导热磁流体动力学方程的柯西问题。我们证明了强解的全局存在性和唯一性，只要数量\（\ Vert \ rho _0 \ Vert _ {L ^ \ infty} + \ Vert b_0 \ Vert _ {L ^ 3} \）适当地小且粘度系数满足\（3 \ mu> \ lambda \）。在此，初始速度和初始温度可能较大。初始密度的假设并不排除初始密度可能在\（{\ mathbb {R}} ^ 3 \）的子集中消失并且它可以是非常紧凑的支持。我们的结果是对Fan和Yu（Nonlinear Anal Real World Appl 10：392–409，2009）和Li等人的工作的扩展。（SIAM J Math Anal 45：1356-1387，2013），分别获得了三维等熵情况下的局部强解和全局强解。该分析基于一些新的数学技术和一些新的有用能量估计。可以将本文视为关于在更高维度的某些大数据类别中无限存在真空的强解的整体存在的第一个结果。