Formal passage from kinetic theory to incompressible Navier-Stokes equations for a mixture of gases

Bisi, Marzia; Desvillettes, Laurent

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1171-1197.

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.

Classification : 82C40, 76P05, 76D05
Mots clés : kinetic theory, incompressible Navier-Stokes equations, hydrodynamic limits

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