Local Well-Posedness to the 2d Cauchy Problem of Full Compressible Magnetohydrodynamic Equations with Vacuum at Infinity ∗

This paper concerns the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in whole plane $\mathbb{R}^2$ with zero density at infinity. By spatial weighted energy method, we derive local existence and uniqueness strong solutions provided that initial magnetic field decay not too slowly Note temperature does need to In particular, vacuum states both interior domain far are allowed.