On the non-resistive limit and the magnetic boundary-layer for one-dimensional compressible magnetohydrodynamics

Abstract

We consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic magnetohydrodynamic (MHD) flows. The non-resistive limit of the global solutions with large data is justified. As a by-product, the global well-posedness of the compressible non-resistive MHD equations is established. Moreover, the thickness of the magnetic boundary-layer of the value with is proved, where is the resistivity coefficient. The proofs of these results are based on a full use of the so-called ‘effective viscous flux’, the material derivative and the structure of the equations.