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arXiv · 1802.04147

Vanishing Shear Viscosity Limit and Boundary Layer Study on the Planar MHD system

Xulong Qin·Tong Yang·Zheng-an Yao·Wenshu Zhou
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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.

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Xulong Qin, Tong Yang, Zheng-an Yao, Wenshu Zhou. 2018-02-09. Vanishing Shear Viscosity Limit and Boundary Layer Study on the Planar MHD system. https://arxiv.org/abs/1802.04147

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