Global Existence And Optimal Decay Rate Of The Compressible Magnetohydrodynamic Equation With Potential Force

In this thesis,we consider the three dimensional compressible viscous magnetohy-drodynamic equations(MHD)with the external potential force.We first derive the corresponding non-constant stationary solutions.Next,we show global well-posedness of the equations,provided the initial data is close to the stationary solution.Finally,based on the elaborate energy estimates for the nonlinear system and LP-Lq decay estimates of the linearized equation,we show the optimal convergence rates of the solution in Lq-norm with 2 ≤ q ≤ 6 and its first derivative in L2-norm when the initial perturbation is bounded in Lp-norm with 1 ≤ p ≤ 6/5.