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A. Jüngel:
"Maxwell-Stefan models for fluid mixtures: derivation, analysis, stochastics";
Vortrag: INdAM workshop "Recent Advances in Kinetic Equations and Applications", Rom (eingeladen); 11.11.2019 - 15.11.2019.

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.