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arXiv · 1910.03279

Perturbative Cauchy theory for a flux-incompressible Maxwell-Stefan system

Marc Briant·Andrea Bondesan
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Abstract

Recently, the authors proved [2] that the Maxwell-Stefan system with an incompressibility-like condition on the total flux can be rigorously derived from the multi-species Boltzmann equation. Similar cross-diffusion models have been widely investigated, but the particular case of a perturbative incompressible setting around a non constant equilibrium state of the mixture (needed in [2]) seems absent of the literature. We thus establish a quantitative perturbative Cauchy theory in Sobolev spaces for it. More precisely, by reducing the analysis of the Maxwell-Stefan system to the study of a quasilinear parabolic equation on the sole concentrations and with the use of a suitable anisotropic norm, we prove global existence and uniqueness of strong solutions and their exponential trend to equilibrium in a perturbative regime around any macroscopic equilibrium state of the mixture. As a by-product, we show that the equimolar diffusion condition naturally appears from this perturbative incompressible setting.

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Marc Briant, Andrea Bondesan. 2019-10-08. Perturbative Cauchy theory for a flux-incompressible Maxwell-Stefan system. https://arxiv.org/abs/1910.03279

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