We present in this paper the formal passage from a kinetic model to the incompressible Navier-Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in terms of the cross sections appearing at the kinetic level.
@article{M2AN_2014__48_4_1171_0,
author = {Bisi, Marzia and Desvillettes, Laurent},
title = {Formal passage from kinetic theory to incompressible Navier-Stokes equations for a mixture of gases},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {48},
year = {2014},
pages = {1171-1197},
doi = {10.1051/m2an/2013135},
mrnumber = {3264350},
zbl = {1301.82046},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2014__48_4_1171_0}
}
Bisi, Marzia; Desvillettes, Laurent. Formal passage from kinetic theory to incompressible Navier-Stokes equations for a mixture of gases. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 48 (2014) pp. 1171-1197. doi : 10.1051/m2an/2013135. http://gdmltest.u-ga.fr/item/M2AN_2014__48_4_1171_0/
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