APPLICATIONS OF MATHEMATICS, Vol. 50, No. 6, pp. 527-541, 2005

A uniqueness result for a model for mixtures
in the absence of external forces
and interaction momentum

Jens Frehse, Sonja Goj, Josef Malek

J. Frehse, S. Goj, University of Bonn, Institute for Applied Mathematics, Beringstr. 6, 53115 Bonn, Germany, e-mails:,; J. Malek, Mathematical Institute, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic, e-mail:

Abstract: We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities $\rho_i$ of the fluids and their velocity fields $u^{(i)}$ are prescribed at infinity: $\rho_i|_{\infty} = \rho_{i \infty} > 0$, $u^{(i)}|_{\infty} = 0$. 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 $\rho_i \equiv\rho_{i \infty}$, $u^{(i)} \equiv0$, $i=1,2$.

Keywords: miscible mixture, compressible fluid, uniqueness, zero force

Classification (MSC 2000): 35Q30, 76N10

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