Global existence and optimal decay rate of the compressible bipolar Navier–Stokes–Poisson equations with external force

In this paper, we consider the three dimensional compressible bipolar 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 coupled elliptic system. Next, we show global well-posedness of the initial value problem for the three dimensional compressible bipolar Navier–Stokes–Poisson equations, provided the prescribed initial date is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L2L2-decay estimates for semigroup generated by the linearized equation, we give the optimal L2L2-convergence rates of the solutions towards the stationary solution.