In this paper, we consider planar magnetohydrodynamics (MHD) system when the viscous coefficients and heat conductivity depend on specific volume v and temperature 𝜃. For technical reasons, the viscous coefficients and heat conductivity are assumed to be proportional to h(v)𝜃^α where h(v) is a non-degenerate smooth function satisfying some additional conditions. We prove the existence and uniqueness of the global-in-time classical solution to the Cauchy problem with general large initial data when |α| is sufficiently small and the coefficient of magnetic diffusion ν is suitably large. Moreover, it is shown that the global solution is asymptotically stable as time tends to infinity.

在本文中，当粘性系数和热导率取决于比容v和温度𝜃时，我们考虑平面磁流体动力学（MHD）系统。由于技术原因，粘性系数和热导率被假定为正比于ħ（v）θ ^α其中ħ（v）是满足一些附加条件的非简并平滑函数。当| | | |时，我们证明了柯西问题的全局及时经典解的存在和唯一性。α | 足够小，磁扩散系数ν适当地大。而且，表明随着时间趋于无穷大，整体解是渐近稳定的。