Global Existence and Decay Rate of Smooth Solutions for Full System of Partial Differential Equations for Three-Dimensional Compressible Magnetohydrodynamic Flows

We focus on the global existence and rates of convergence for the compressible magnetohydrodynamic equations in . We prove the global existence of smooth solutions using the standard energy method under the condition that the initial data are close to a constant equilibrium state in . Rates of convergence for the solution in norm with and its first- and second-order derivatives in norm are obtained, if the initial data belong to with .