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

Abstract

In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations in R 3 . 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 H 3 -framework. Moreover, if additionally the initial data belong to L p with 1 ≤ p < 6 5 , the optimal convergence rates of the solutions in L q -norm with 2 ≤ q ≤ 6 and its spatial derivatives in L 2 -norm are obtained.