1. Vanishing Shear Viscosity Limit and Boundary Layer Study on the Planar MHD system
- Author
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Qin, Xulong, Yang, Tong, Yao, Zheng-an, and Zhou, Wenshu
- Subjects
Mathematics - Analysis of PDEs ,FOS: Mathematics ,35B40, 35B45, 76N10, 76N20, 76W05, 76X05 ,Analysis of PDEs (math.AP) - Abstract
We consider an initial boundary problem for the planar MHD system under the general condition on the heat conductivity $\kappa$ that may depend on both the density $\rho$ and the temperature $\theta$ satisfying $\kappa(\rho,\theta)\geq\kappa_1 \theta^{q}$ for some constants $\kappa_1>0$ 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., Comment: 31 pages. arXiv admin note: text overlap with arXiv:1511.00201
- Published
- 2018
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