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Maxwell-Stefan diffusion limit for gas mixtures

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Joint Analysis / Applied Mathematics Seminar

In this talk, we study the Boltzmann-like equations modelling the mixture of ideal monatomic inert gases subject to inter-molecular elastic collison interactions. Under parabolic scaling, we study this system of Boltzmann equations in the vanishing Mach and Knudsen numbers limit. In this limit, we show that the local densities associated with the scaled Boltzmann equations approximate solutions to the Maxwell-Stefan diffusion equations. We obtain explicit expressions for the binary diffusion coefficients in the Maxwell-Stefan system purely in terms of the mechanical data associated with the collision interactions. We shall comment on the Cauchy theory for the system of Boltzmann equations and the Maxwell-Stefan system of equations.

We shall also briefly overview the wide range of open problems in connection to the sixth problem of Hilbert for the system of Boltzmann equations which concerns their asymptotic behaviour in the limit as the mean free path tends to zero. Different asymptotic regimes leading to compressible and incompressible fluid limits will be highlighted.

The results presented in this talk are from a joint work with Francesco Salvarani (Pavia and Paris-Dauphine).

This talk is part of the Analysis Seminar series.

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