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Long time behavior of weak solutions to Navier-Stokes-Poisson system. (English) Zbl 1294.35058
Summary: B. Ducomet et al. [Discrete Contin. Dyn. Syst. 11, No. 1, 113–130 (2004; Zbl 1080.35068)] showed the existence of global weak solutions to the Navier-Stokes-Poisson system. We study the global behavior of such a solution. This is done by (1) proving uniqueness of a solution to the stationary system; (2) by showing convergence of a weak solution to the stationary solution. In (1) we consider only the case with repulsion. We prove our result in the case of a bounded domain with smooth boundary in \({\mathbb{R}^3}\) and also in the case of the whole space \({\mathbb{R}^3}\).

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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