Diffusion asymptotics of a kinetic model for gaseous mixtures

Laurent Boudin; Bérénice Grec; Milana Pavić; Francesco Salvarani

doi:10.3934/krm.2013.6.137

Article Contents

2013, Volume 6, Issue 1: 137-157. Doi: 10.3934/krm.2013.6.137

This issue Previous Article Mathematical theory and numerical methods for Bose-Einstein condensation Next Article Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials

Diffusion asymptotics of a kinetic model for gaseous mixtures

1.
UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005
2.
MAP5, CNRS UMR 8145, Université Paris Descartes, Sorbonne Paris Cité, 45 Rue des Saints Pères, F-75006 Paris
3.
CMLA, ENS Cachan, PRES UniverSud Paris, 61 Avenue du Président Wilson, F-94235 Cachan Cedex
4.
Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1 - 27100 Pavia

Received: June 30, 2012

Revised: September 30, 2012

Published: February 2013

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Abstract

In this work, we consider the non-reactive fully elastic Boltzmann equations for mixtures in the diffusive scaling. We mainly use a Hilbert expansion of the distribution functions. After briefly recalling the H-theorem, the lower-order non trivial equality obtained from the Boltzmann equations leads to a linear functional equation in the velocity variable. This equation is solved thanks to the Fredholm alternative. Since we consider multicomponent mixtures, the classical techniques introduced by Grad cannot be applied, and we propose a new method to treat the terms involving particles with different masses.

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Mathematics Subject Classification: Primary: 35Q20, 45B05; Secondary: 35Q35, 82C40.

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