LOCAL WELL-POSEDNESS TO THE FULL COMPRESSIBLE MHD EQUATIONS WITHOUT INITIAL COMPATIBILITY CONDITIONS

This paper is concerned with the Cauchy problem of two dimensional full compressible magnetohydrodynamic (MHD) equations with vacuum. It is shown that if the initial data satisfies the weaker regularities and does not need to meet any compatibility conditions, the unique local-in-time strong solution to the MHD equations exists. Note that the vacuum initial state at the interior domain is allowed. Particularly, by leveraging and simplifying the method in [J. Li and Y. Zheng, J. Math. Fluid Mech., 25 (2023), 14], we generalize their results to the MHD equations.