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Diffusion asymptotics of a kinetic model for gaseous mixtures

Laurent Boudin 1, 2, Bérénice Grec 1, 3, Milana Pavic 4, 5, Francesco Salvarani 6

(2012-06-06)

In this work, we investigate the asymptotic behaviour of the solutions to the non-reactive fully elastic Boltzmann equations for mixtures in the diffusive scaling. We deal with cross sections such as hard spheres or cut-off power law potentials. We use Hilbert expansions near the common thermodynamic equilibrium granted by the H-theorem. The lower-order non trivial equality obtained from the Boltzmann equations leads to a linear functional equation in the velocity variable which 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. The next-order equality in the Hilbert expansion then allows to write the macroscopic continuity equations for each component of the mixture.

1:	REO (INRIA Paris-Rocquencourt)
	INRIA – Laboratoire Jacques-Louis Lions
2:	Laboratoire Jacques-Louis Lions (LJLL)
	CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
3:	Mathématiques appliquées Paris 5 (MAP5)
	CNRS : UMR8145 – Université Paris V - Paris Descartes
4:	Centre de Mathématiques et de Leurs Applications (CMLA)
	CNRS : UMR8536 – École normale supérieure de Cachan - ENS Cachan
5:	Department of Mathematics and Informatics [Novi Sad]
	University of Novi Sad
6:	Dipartimento di matematica F. Casorati
	Università degli studi di Pavia

Subject

:

Mathematics/Analysis of PDEs

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From: Bérénice Grec <>

Submitted on: Wednesday, 6 June 2012 15:35:30

Updated on: Wednesday, 6 June 2012 16:50:22