A Uniqueness Result for a Model for Mixtures in the Absence of External Forces and Interaction Momentum

We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities ϱi of the fluids and their velocity fields u(i) are prescribed at infinity: ϱ i|∞ = ϱi∞ > 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 ϱi ≡ ϱi∞, u(i) ≡ 0, i = 1, 2.

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