Global Classical Solutions to 3D Compressible Magnetohydrodynamic Equations with Large Oscillations and Vacuum

Abstract

We consider the Cauchy problem of three-dimensional isentropic compressible magnetohydrodynamic equations in the present paper. For regular initial data with small energy but possibly large oscillations, we prove the global well-posedness of classical solution, where the flow density is allowed to contain vacuum states, and the large-time behavior of the solution is also shown.