Global Existence And Large-time Behavior Of Smooth Solutions For The Three-dimensional Compressible MHD/Vlasov-Fokker-Planck Equations

In this paper,we consider the global existence and large time behavior of smooth solutions for the Cauchy problem of the three-dimensional fluid parti-cle coupled model.The equations are composed of the Vlasov-Fokker-Planck equation and the compressible magnetic fluid equation through friction cou-pling.Assuming that ?(n0,u0,B0)?H3+?f0?L?2(Hx3)is small enough,the global existence of smooth solutions to the Cau chy problem is obtained by using the energy method.Further assume ?(n0,u0,B0)?Lx1+?f0?L?2(Lx1)is small enough,the algebraic decay rate of the solutions is obtained by using Fourier analysis technique.This paper introduces it through the following two parts:In Chapter 1,we introduce some related backgrounds about the results of the global well-posedness the to the fluid-particle model both at home and abroad;In Chapter 2,under the assumption that the initial disturbance is small e-nough,we obtain a priori estimation based on the energy method and obtain the existence of global solution by using the existence of local solution and continuity method.Next,we use the Fourier analy sis technique and standard thermonu-clear knowledge to obtain the algebraic decay estimates of the corresponding linear equations.Finally,the solutions of the nonlinear problem is expressed by Duhamel's principle,and the attenuation of the solutions is obtained by com-bining with the previous estimation.