Stationary Solutions to an Inflow Problem for a Compressible Model of the Viscous Ions Motion

In this paper, we study the stationary solutions of the inflow problem for a compressible model of the viscous ions motion, which is given by the one-dimensional isentropic compressible Navier–Stokes–Poisson equations. The unique existence of the stationary solutions to the one-dimensional isentropic compressible Navier–Stokes–Poisson equations in the half line is shown provided that the boundary data satisfy some smallness conditions. Moreover, the spatial decay rates of the stationary solutions are presented. By taking the accurate analysis of the cubic characteristic equation for the linearized stationary system, the sign of the real part corresponding to the eigenvalues can be sure. Then our results can be proven by the manifold theory and the center manifold theorem.