平面MHD体系的消失剪切粘度极限和边界层研究
Vanishing Shear Viscosity Limit and Boundary Layer Study on the Planar MHD system
摘要：
在导热系数$κ$可能依赖于密度$ρ$和温度$θ$的一般条件下，考虑平面MHD系统的初边值问题，对于某些常数$κ_1>0$和$q>0.$，满足$κ(ρ,θ)\geqκ_1 θ^{q}$.首先，得到了大初值下强解的整体存在性，然后证明了剪切粘性消失的极限.此外，还得到了$L^2$的收敛速度和边界层厚度的估计。
英文摘要：
We consider an initial boundary problem for the planar MHD system under the general condition on the heat conductivity $κ$ that may depend on both the density $ρ$ and the temperature $θ$ satisfying $κ(ρ,θ)\geqκ_1 θ^{q}$ for some constants $κ_1>0$ and $q>0.$ Firstly, the global existence of strong solution for large initial data is obtained, and then the limit of the vanishing shear viscosity is justified. In addition, the $L^2$ convergence rate is obtained together with the estimation on the thickness of the boundary layer.
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