粘性依赖于温度的MHD方程组整体经典解的正则性  

Global Regularity of Classical Solutions to the Planar MHD Equations with Temperature-dependent Viscosity

作　　者：尚朝阳 任凯芳 唐福全 Zhao Yang SHANG;Kai Fang REN;Fu Quan TANG(School of Finance,Shanghai Lixin University of Accounting and Finance,Shanghai 201209,P.R.China;School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,P.R.China)

机构地区：[1]上海立信会计金融学院金融学院,上海201209 [2]上海交通大学数学科学学院,上海200240

出　　处：《数学学报（中文版）》2021年第1期1-40,共40页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11571232,11831011)。

摘　　要：本文主要研究可压缩非等熵平面磁流体动力学方程组的Cauchy问题整体经典解的正则性,其中方程组的粘性系数λ,μ,磁扩散系数η和热传导系数κ都是比容v和温度θ的函数,正比于h(v)θα,h是满足一定条件的非退化光滑函数.在正则性准则■的条件下,当α适当小时,我们证明了大初值整体经典解的存在性.We study the global regularity of classical solutions to the Cauchy problem of planar magnetohydrodynamics equations when the viscosity coefficients λ,μ,magnetic diffusion coefficient η and the heat conductivity coefficient κ depend on the specific volume v and the temperature θ which are proportional to h(v)θ~α for certain non-degenerate smooth function h.Under the condition of regularity criterion ■,when α is small,we prove the existence of global classical solution with large initial data.

关 键 词：MHD方程组 粘性依赖于温度 正则性准则 整体经典解 

分 类 号：O175.2[理学—基础数学]