Strong solutions to the Cauchy problem of the two-dimensional non-baratropic non-resistive magnetohydrodynamic equations with zero heat conduction

Abstract

This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy estimates, we prove that there exists a local strong solution provided the initial density and the initial magnetic decay not too slow at infinity.