A Uniqueness Result for a Model for Mixtures in the Absence of External Forces and Interaction Momentum |
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Authors: | Jens Frehse Sonja Goj Josef Malek |
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Institution: | (1) Institute for Applied Mathematics, University of Bonn, Beringstr. 6, 53115 Bonn, Germany;(2) Mathematical Institute, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic |
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Abstract: | We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities ϱ
i
of the fluids and their velocity fields u
(i) are prescribed at infinity: ϱ
i
|∞ = ϱ
i∞ > 0, u
(i)|∞ = 0. Neglecting the convective terms, we have proved earlier that weak solutions to such a reduced system exist. Here we
establish a uniqueness type result: in the absence of the external forces and interaction terms, there is only one such solution,
namely ϱ
i
≡ ϱ
i∞, u
(i) ≡ 0, i = 1, 2.
This work was supported by the SFB 611 at the University of Bonn and the European HYKE network (contract no. HPRN-CT-2002-00282).
The third author was also supported by the project CSF 201/03/0934, and by MSM 0021620839. |
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Keywords: | miscible mixture compressible fluid uniqueness zero force |
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