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 andLp−Lqrates of convergence for the compressible magnetohydrodynamic equations inR3. 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 inH3. Rates of convergence for the solution inLqnorm with2≤q≤6and its first- and second-order derivatives inL2norm are obtained, if the initial data belong toLpwith1≤p≤65.