The Stability Of Stationary Solution For Outflow Problem On The Navier-Stokes-Poisson System

In this thesis, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence of sta-tionary solution by the method of eigenvalue analysis and stable manifold theorem. We obtain the asymptotic stability of solution by the method of energy method. We ob-tain the convergence rate of solution towards stationary solution by the weighted energy method. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time.