Stability for the $2\frac12$-D compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow

Abstract: In this paper, we are concerned with the initial boundary values problem associated to the compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow, where the magnetic field is vertical. More precisely, by exploiting the intrinsic structure of the system and introducing several new unknown quantities, we overcome the difficulty stemming from the lack of dissipation for density and magnetic field, and prove the global well-posedness of strong solutions in the framework of Soboles spaces $H^3$. In addition, we also get the exponential decay for this non-resistive system. Different from the known results [23], [24], [42], we donot need the assumption that the background magnetic field is positive here.