Geodesic
Formal passage from kinetic theory to incompressible Navier-Stokes equations for a mixture of gases
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1171-1197

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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.

DOI : 10.1051/m2an/2013135
Classification : 82C40, 76P05, 76D05
Keywords: kinetic theory, incompressible Navier-Stokes equations, hydrodynamic limits 
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     title = {Formal passage from kinetic theory to incompressible {Navier-Stokes} equations for a mixture of gases},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1171--1197},
     publisher = {EDP-Sciences},
     volume = {48},
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     year = {2014},
     doi = {10.1051/m2an/2013135},
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     zbl = {1301.82046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013135/}
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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 , Tome 48 (2014) no. 4, pp. 1171-1197. doi: 10.1051/m2an/2013135

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