The Maxwell-Stefan Diffusion Limit for a Kinetic Model of Mixtures

We consider the non-reactive elastic Boltzmann equation for multicomponent gaseous mixtures. We deduce, under the standard diffusive scaling, that well prepared initial conditions lead to solutions satisfying the Maxwell-Stefan diffusion equations in the vanishing Mach and Knudsen numbers limit.

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Bibliographic Details
Published in:	Acta applicandae mathematicae Vol. 136; no. 1; pp. 79 - 90
Main Authors:	Boudin, Laurent, Grec, Bérénice, Salvarani, Francesco
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01-04-2015 Springer Nature B.V Springer Verlag
Subjects:	Analysis of PDEs Applications of Mathematics Boltzmann equation Boltzmann transport equation Calculus of Variations and Optimal Control; Optimization Chemical reactions Computational Mathematics and Numerical Analysis Diffusion Gases Initial conditions Kinetics Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Partial Differential Equations Probability Theory and Stochastic Processes Studies Gaseous mixture Maxwell-Stefan equations Boltzmann equations Diffusion limit
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Summary:	We consider the non-reactive elastic Boltzmann equation for multicomponent gaseous mixtures. We deduce, under the standard diffusive scaling, that well prepared initial conditions lead to solutions satisfying the Maxwell-Stefan diffusion equations in the vanishing Mach and Knudsen numbers limit.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0167-8019 1572-9036
DOI:	10.1007/s10440-014-9886-z