发表机构
Nanchang University（南昌大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究无界域上一维平面可压缩磁流体动力学方程，在黏性退化且热导率幂律下，对任意大初值建立全局强解的存在唯一性，并证明解随时间趋于平衡态。
AI 中文摘要
本文在无界域上研究一维平面可压缩磁流体动力学系统。纵向黏性系数服从比容的幂律，允许其在密度接近真空时退化，热导率服从温度的幂律。对于热导率项中任意固定的非负指数，只要黏性系数的正指数足够小，即可对任意大的初始数据建立全局强解的存在唯一性。比容和温度具有与时间无关的上下界。此外，对于每个允许的黏性指数，当时间趋于无穷时，解在空间上一致收敛到平衡态。
英文摘要
The one-dimensional planar compressible magnetohydrodynamic system is studied on unbounded domains. The longitudinal viscosity obeys a power law of the specific volume, which permits it to degenerate as the density approaches vacuum, and the heat conductivity follows a power law of the temperature. For any fixed non-negative exponent in the heat conductivity term, the existence and uniqueness of global strong solutions are established for arbitrarily large initial data, provided that the positive exponent for viscosity is sufficiently small. The specific volume and temperature possess time-independent upper and lower bounds. Moreover, for each admissible viscosity exponent, the solution converges uniformly in space to the equilibrium state as time tends to infinity.
