Article
MSC:
35D05,
35Q30,
35Q35,
76D03,
76D07,
76N10,
76T99 | MR 2181024 | Zbl 1099.35079 | DOI: 10.1007/s10492-005-0035-x
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Keywords:
miscible mixture; compressible fluid; uniqueness; zero force
miscible mixture; compressible fluid; uniqueness; zero force
Summary:
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 $\rho _i \equiv \rho _{i \infty }$, $u^{(i)} \equiv 0$, $i=1,2$.
References:
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