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

Jens FrehseSonja GojJosef Málek — 2005

Applications of Mathematics

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 .

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