Stability of stationary solutions to the inflow problem for the two-fluid non-isentropic Navier–Stokes–Poisson system

Abstract

In this paper, we study the asymptotic behavior of solution to the initial boundary value problem for the two-fluid non-isentropic Navier–Stokes–Poisson system in a half line (0,∞). We consider an inflow problem where the gas enter into the region through the boundary for general gases including ideal polytropic gas. On account of the quasineutral assumption and the absence of the electric field for the large time behavior, we show the existence of the stationary solutions with the aid of the center manifold theory, and then we give the rigorous proof of the stability theorem on the stationary solutions under small perturbations for the corresponding initial boundary value problem of the Navier–Stokes–Poisson system. Note that it is the first result for the stability of nonlinear waves on the inflow problem of the Navier–Stokes–Poisson system.