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

Frehse, Jens ; Goj, Sonja ; Málek, Josef

Applications of Mathematics, Tome 50 (2005) no. 6, pp. 527-541.

Résumé

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 $\rho _i \equiv \rho _{i \infty }$, $u^{(i)} \equiv 0$, $i=1,2$.

Détail

DOI : 10.1007/s10492-005-0035-x

Classification : 35D05, 35Q30, 35Q35, 76D03, 76D07, 76N10, 76T99
Keywords: miscible mixture; compressible fluid; uniqueness; zero force