Global well-posedness and time-decay for the full compressible non-resistive MHD equations in a 3D infinite slab

Abstract

This paper is concerned with the global well-posedness and time-decay of the system of full compressible viscous non-resistive MHD fluids in a three-dimensional horizontally infinite slab with finite height. We reformulate our analysis to Lagrangian coordinates, and then develop a new mathematical approach to establish global well-posedness of the MHD system, which requires no compatibility conditions on the initial data.