On vanishing limits of the shear viscosity and Hall coefficients for the planar compressible Hall‐MHD system

Abstract

This paper deals with an initial‐boundary value problem of the planar compressible Hall‐magnetohydrodynamic (for short, Hall‐MHD) equations. For the fixed shear viscosity and small Hall coefficients, we obtain the existence of long‐time strong solutions of Hall‐MHD equations and corresponding MHD equations. As both the shear viscosity and the Hall coefficients tend to zero, the convergence rate for the solutions from Hall‐MHD equations to MHD equations is given. The thickness of boundary layer is discussed by spatial weighted estimate and the characteristic of boundary layer is described by constructing a boundary layer function.