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

Abstract

We focus on the global existence and$L^p-L^q$rates of convergence for the compressible magnetohydrodynamic equations in$R^3$. 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$H^3$. Rates of convergence for the solution in$L^q$norm with$2\le q\le 6$and its first- and second-order derivatives in$L^2$norm are obtained, if the initial data belong to$L^p$with$1\le p\le \frac{6}{5}$.