Local existence of compressible MHD equations without initial compatibility conditions

In this paper, we study the initial-boundary value problem of three-dimensional viscous, compressible, and heat conductive magnetohydrodynamic equations. Local existence and uniqueness of strong solutions is established with any such initial data that the initial compatibility conditions do not be required. The analysis is based on some suitable prior estimates for the strong coupling term u ·∇ H and strong nonlinear term curl H × H . Our proof of the existence and uniqueness of solutions is in the Lagrangian coordinates first and then transformed back to the Euler coordinates.