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

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  • In this paper, we are concerned with the initial boundary value problem on the two-fluid Navier-Stokes-Poisson system in the half-line $R_+$. We establish the global-in-time asymptotic stability of the rarefaction wave and the boundary layer both for the outflow problem under the smallness assumption on initial perturbation, where the strength of the rarefaction wave is not necessarily small while the strength of the boundary layer is additionally supposed to be small. Here, the large initial data with densities far from vacuum is also allowed in the case of the non-degenerate boundary layer. The results show that the large-time behavior of solutions coincides with the one for the single Navier-Stokes system in the absence of the electric field. The proof is based on the classical energy method. The main difficulty in the analysis comes from the slower time-decay rate of the system caused by the appearance of the electric field. To overcome it, we use the coupling property of the two-fluid equations to capture the dissipation of the electric field interacting with the nontrivial asymptotic profile.
    Mathematics Subject Classification: 76X05, 35M33, 35M35, 35B40.

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