BIRS Workshop Lecture Videos
Analysis of degenerate cross-diffusion systems for heat-conducting fluid mixtures Juengel, Ansgar
We present global-in-time existence results for two cross-diffusion systems modeling
heat-conducting fluid mixtures. Both models consist of the balance equations for the
mass densities and temperature. The key difficulty is the nonstandard degeneracy in the
diffusion (Onsager) matrices, i.e., ellipticity is lost when the fluid density or
temperature vanishes. This problem is overcome in the first model by exploiting the
volume-filling property of the mixture, leading to gradient estimates for the square
root of the partial densities, and in the second model by compensated compactness
and renormalization techniques from mathematical fluid dynamics.
The first model is joint work with C. Helmer, the second one with G. Favre, C. Schmeiser, and N. Zamponi.
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