Paper detail

Vanishing shear viscosity limit and boundary layer for the one-dimensional full compressible MHD equations with large data

This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The vanishing shear viscosity limit is justified and the convergence rates are obtained. To capture the behavior of the solutions at small shear viscosity, we also discuss the boundary-layer thickness and the boundary-layer solution. As by-products, the global well-posedness of strong solutions with large data is established. The proofs are based on the global (uniform) estimates which are achieved by making a full use of the "effective viscous flux", the material derivatives and the structure of the one-dimensional equations. Moreover, the lower positive bound of the density is obtained by using some new ideas, which are rather different from those in the existing literature.