Solution Research Of Compressible Viscous Magnetohydrodynamic Equations(MHD)

In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations(MHD) with the external potential force. We first derive the corresponding non-constant stationary solutions. Then, we show global well-posedness and the optimal decay rate of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided the prescribed initial data is close to the stationary solution. The paper is organized as follows:The first chapter, we introduce the background of our research and main topics that we will study in the following chapters.The second chapter, we mainly do some preparation work for the fourth chapter and analysis some fundamental estimates of the linear MHD equations with Lorentz space.The third chapter, we combine the existence of solutions of linear equations and the contraction mapping to prove the existence of stationary solution; then establish the priori estimate to prove the existence of global solution.The fourth chapter, we analyze the decay estimates of global solutions on the basis of the second chapter.