A. Jüngel:

"Maxwell-Stefan models for fluid mixtures: derivation, analysis, stochastics";

Talk: INdAM workshop "Recent Advances in Kinetic Equations and Applications", Rom (invited); 2019-11-11 - 2019-11-15.

Ansgar Juengel

Maxwell-Stefan models for fluid mixtures: derivation, analysis, stochastics

The Maxwell-Stefan equations describe the dynamics of

fluid mixtures in a diffusive regime. Examples include heliox for asthma, ion transport in biological membranes, and dynamics of lithium-ion batteries.

Maxwell-Stefan systems consist of cross-dffusion equations with generally nonsymmetric, indefinite

diffusion matrices. Written in terms of chemical potentials or entropy variables, the diffusion matrix of

the transformed system (the so-called Onsager matrix) becomes symmetric and positive semi-definite,

which is the starting point for the analysis.

In this talk, we present some approaches to derive the Maxwell-Stefan equations rigorously from Boltzmann

systems in the diffusion limit or from Euler

flow systems in the high-friction limit. We recall some

results on the existence of global weak solutions, using the boundedness-by-entropy method, and extend

this method to Maxwell-Stefan systems with stochastic forcing.

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