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.
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