On classical solutions to the Cauchy problem of the 2D compressible non-resistive MHD equations with vacuum states

Abstract

In this paper, we investigate the Cauchy problem of the compressible non-resistive MHD on with a vacuum as the far field density. We prove that the two-dimensional (2D) Cauchy problem has a unique local strong solution provided that the initial density and magnetic field decay are not too slow at infinity. Furthermore, if the initial data satisfies some additional regularity and compatibility conditions, the strong solution becomes a classical one. Additionally, we establish a blowup criterion for the 2D compressible non-resistive MHD depending solely on the density and magnetic fields.