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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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