Existence and optimal decay rates of the compressible non-isentropic Navier-Stokes-Poisson models with external forces

In this paper, we consider the three dimensional compressible non-isentropic Navier-Stokes-Poisson equations with the potential external force. Under the smallness assumption of the external force in some Sobolev space, the existence of the stationary solution is established by solving a nonlinear elliptic system. Next, we show global well-posedness of the initial value problem for the three dimensional compressible nonisentropic Navier-Stokes-Poisson equations, provided the prescribed initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L-2-decay estimates for the semigroup generated by the linearized equation, we give the optimal L-2-convergence rates of the solutions toward the stationary solution. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.