Volume 48, Number 4, July-August 2014
|Page(s)||1171 - 1197|
|Published online||15 July 2014|
Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases
Dip. di Matematica e Informatica, Università di Parma,
Parco Area delle Scienze
2 CMLA, ENS Cachan, CNRS, 61, Av. du Pdt Wilson, 94235 Cachan cedex, France
Received: 30 November 2012
Revised: 11 June 2013
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.
Mathematics Subject Classification: 82C40 / 76P05 / 76D05
Key words: Kinetic theory / incompressible Navier–Stokes equations / hydrodynamic limits
© EDP Sciences, SMAI, 2014
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