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 Lp−Lq rates of convergence for the compressible magnetohydrodynamic equations in R3. 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 H3. Rates of convergence for the solution in Lq norm with 2≤q≤6 and its first- and second-order derivatives in L2 norm are obtained, if the initial data belong to Lp with 1≤p≤65.