Stability of rarefaction wave and boundary layer for outflow problem on the two-fluid Navier-Stokes-Poisson equations

Abstract

In this paper, we are concerned with the initial boundary valueproblem on the two-fluid Navier-Stokes-Poisson system in thehalf-line $R_+$. We establish the global-in-time asymptoticstability of the rarefaction wave and the boundary layer both forthe outflow problem under the smallness assumption on initialperturbation, where the strength of the rarefaction wave is notnecessarily small while the strength of the boundary layer isadditionally supposed to be small. Here, the large initial data withdensities far from vacuum is also allowed in the case of thenon-degenerate boundary layer. The results show that the large-timebehavior of solutions coincides with the one for the singleNavier-Stokes system in the absence of the electric field. The proofis based on the classical energy method. The main difficulty in theanalysis comes from the slower time-decay rate of the system causedby the appearance of the electric field. To overcome it, we use thecoupling property of the two-fluid equations to capture thedissipation of the electric field interacting with the nontrivialasymptotic profile.