Well-posedness for compressible MHD systems with highly oscillating initial data

In this paper, a unique local solution for compressible magnetohydrodynamics systems has been constructed in the critical Besov space framework by converting the system in Euler coordinates to a system in Lagrange coordinates. Our results improve the range of the Lebesgue exponent in the Besov space from [2, N) to [2,2N), where N denotes the space dimension. Then, we give a lower bound for the maximal existence time, which is important for our construction of global solutions. Based on the lower bound, we use the effective viscous flux and Hoff's energy method to obtain the unique global solution, which allows the initial velocity field and the magnetic field to have large energies and allows the initial density to exhibit large oscillations on a set of small measure. Published by AIP Publishing.