STABILITY OF THE MAXWELL-STEFAN SYSTEM IN THE DIFFUSION ASYMPTOTICS OF THE BOLTZMANN MULTI-SPECIES EQUATION - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

STABILITY OF THE MAXWELL-STEFAN SYSTEM IN THE DIFFUSION ASYMPTOTICS OF THE BOLTZMANN MULTI-SPECIES EQUATION

Andrea Bondesan
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  • PersonId : 974939
Marc Briant
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  • PersonId : 1048449

Résumé

We investigate the diffusion asymptotics of the Boltzmann equation for gaseous mixtures, in the perturbative regime around a local Maxwellian vector whose fluid quantities solve a flux-incompressible Maxwell-Stefan system. Our framework is the torus and we consider hard-potential collision kernels with angular cutoff. As opposed to existing results about hydrodynamic limits in the mono-species case, the local Maxwellian we study here is not a local equilibrium of the mixture due to cross-interactions. By means of a hypocoercive formalism and introducing a suitable modified Sobolev norm, we build a Cauchy theory which is uniform with respect to the Knudsen number ε. In this way, we shall prove that the Maxwell-Stefan system is stable for the Boltzmann multi-species equation, ensuring a rigorous derivation in the vanishing limit ε → 0.
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Dates et versions

hal-02320041 , version 1 (18-10-2019)

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  • HAL Id : hal-02320041 , version 1

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Andrea Bondesan, Marc Briant. STABILITY OF THE MAXWELL-STEFAN SYSTEM IN THE DIFFUSION ASYMPTOTICS OF THE BOLTZMANN MULTI-SPECIES EQUATION. 2019. ⟨hal-02320041⟩
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