Stationary waves to the two-fluid non-isentropic Navier-Stokes-Poisson system in a half line: Existence, stability and convergence rate

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Abstract

In this paper, we study the asymptotic behavior of solution tothe initial boundary value problem for the two-fluid non-isentropicNavier-Stokes-Poisson system in a half line$\mathbb{R}_{+}:=(0,\infty).$ Our idea mainly comes from[10] which describes the large time behavior of solutionfor the non-isentropic Navier-Stokes equations in a half line. Theelectric field brings us some additional troubles compared withNavier-Stokes equations in the absence of the electric field. Weobtain the convergence rate of global solution towardscorresponding stationary solution. Precisely, if an initialperturbation decays with the algebraic or the exponential rate inspace, the solution converges to the corresponding stationarysolution as time tends to infinity with the algebraic or theexponential rate in time. The proofs are given by a weighted energymethod.

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