Asymptotic Stability Of The Solution To Euler-Vlasov-Fokker-Planck Equation With External Forces

We consider the Cauchy problem of the Vlasov-Fokker-Planck equation for the dis?persed phase coupled to the incompressible Euler equations with external forces,There are three chapters in this thesis.In the first chapter,we introduce the physical background,research significance and some known results of the equations.Furthermore,we give the main results of this thesis.In the second chapter,combined with macro-micro decomposition,we prove the global existence of solutions by using classical energy method.In the third chapter,by applying the estimate of the linearized equations,we obtain the decay rate of the solutions to the background profile,which is the same to the decay rate for the corresponding system without external forces.