Decay Rate Of Three-dimensional Bipolar Navier-stokes-poisson Equations

In this paper, we show the large behavior of the bipolar Navier-Stokes-Poisson.and the existence of the classical solutions of the bipolar Navier-Stokes-Poisson with the small initial data. And prove that the density of bipolar Navier-Stokes-Poisson system converges to its equilibrium state at the L²-rate (1+t)^?, which is same as the compressible Navier-Stokes system, but the momentum (or velocity) decays at L²-rate (1+t)^?. These convergence rates are also shown to be optimal. Generalize the result in [1] to the the bipolar Navier-Stokes-Poisson.