Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 382, Issue 1, Pages 381-440Publisher
SPRINGER
DOI: 10.1007/s00220-021-03976-5
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- Universite Sorbonne Paris Cite [ANR-11-IDEX-0005]
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This study investigates the diffusion asymptotics of the Boltzmann equation for gaseous mixtures in a perturbative regime around a local Maxwellian vector. By introducing a suitable modified Sobolev norm and utilizing a hypocoercive formalism, a Cauchy theory that is uniform with respect to the Knudsen number epsilon is established. It is proven that the Maxwell-Stefan system is stable for the Boltzmann multi-species equation, ensuring a rigorous derivation in the vanishing limit epsilon -> 0.
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 epsilon. 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 epsilon -> 0.
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