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 $1\le p\le \frac{6}{5}$ .