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

Frehse, Jens, Goj, Sonja, and Málek, Josef. "A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum." Applications of Mathematics 50.6 (2005): 527-541. <http://eudml.org/doc/33236>.

@article{Frehse2005,
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 $\rho _i \equiv \rho _\{i \infty \}$, $u^\{(i)\} \equiv 0$, $i=1,2$.},
author = {Frehse, Jens, Goj, Sonja, Málek, Josef},
journal = {Applications of Mathematics},
keywords = {miscible mixture; compressible fluid; uniqueness; zero force; miscible mixture; compressible fluid; uniqueness; zero force},
language = {eng},
number = {6},
pages = {527-541},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum},
url = {http://eudml.org/doc/33236},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Frehse, Jens
AU - Goj, Sonja
AU - Málek, Josef
TI - A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 6
SP - 527
EP - 541
AB - 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 $\rho _i \equiv \rho _{i \infty }$, $u^{(i)} \equiv 0$, $i=1,2$.
LA - eng
KW - miscible mixture; compressible fluid; uniqueness; zero force; miscible mixture; compressible fluid; uniqueness; zero force
UR - http://eudml.org/doc/33236
ER -