Global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamic equations

In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations in R3R3. We prove the global existence of the smooth solutions by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H3H3-framework. Moreover, if additionally the initial data belong to LpLp with 1≤p<65, the optimal convergence rates of the solutions in LqLq-norm with 2≤q≤62≤q≤6 and its spatial derivatives in L2L2-norm are obtained.