Stability of the stationary solution to an outflow problem for the bipolar quantum Navier-Stokes-Poisson equations

This paper is concerned with the asymptotic behavior of solutions to an outflow problem for one-dimensional bipolar quantum Navier-Stokes-Poisson equations in half space. First, by means manifold theory and center theorem, we show existence spatial decay rate stationary solution provided boundary strength small enough. Next, based on elaborate energy estimates, prove that asymptotically stable case initial perturbation around are sufficiently small.