On the behavior of boundary layers of one-dimensional isentropic planar MHD equations with vanishing shear viscosity limit

In this paper, we consider an initial-boundary value problem for the one-dimensional equations of planar isentropic magnetohydrodynamics (MHD). The vanishing shear viscosity limit is justified. More important, both the thickness and the behavior of boundary layers are described. The proofs of these results are based on the full use of the material derivative, the “effective viscous flux”, and the mathematical structure of the equations.