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

Published online by Cambridge University Press:  15 July 2014

Marzia Bisi  and
Laurent Desvillettes
Marzia Bisi
Affiliation:
Dip. di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy. [email protected]
Laurent Desvillettes
Affiliation:
CMLA, ENS Cachan, CNRS, 61, Av. du Pdt Wilson, 94235 Cachan cedex, France; [email protected]
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Abstract

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.

Keywords

Kinetic theoryincompressible Navier–Stokes equationshydrodynamic limits
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 4 , July 2014 , pp. 1171 - 1197
Copyright
© EDP Sciences, SMAI, 2014

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