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Global Large Solutions to the Cauchy Problem of Planar Magnetohydrodynamics Equations with Temperature-Dependent Coefficients
Journal of Dynamical and Control Systems ( IF 0.6 ) Pub Date : 2021-01-19 , DOI: 10.1007/s10883-020-09526-x
Zhaoyang Shang

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)𝜃α 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.



中文翻译:

具有温度相关系数的平面磁流体动力学方程的柯西问题的全局大解

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ħvθ α其中ħv)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。

更新日期:2021-02-02
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