Optimal convergence rate of the vanishing shear viscosity limit for one-dimensional isentropic planar MHD equations

In this paper, we consider the initial-boundary value problem for the one-dimensional isentropic planar magnetohydrodynamics (MHD) equations. Using asymptotic expansions, we study the expression of the boundary layer and the rate of convergence of the vanishing shear viscosity limit, which optimizes the convergence rate ${\epsilon }^{1/4}$ of the results presented in reference Ye and Zhang [35] (2016) to ${\epsilon }^{1/2}$.