M. Bulicek, A. Jüngel, M. Pokorny, N. Zamponi:

"Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures";

in: "ASC Report 2/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 62.

The existence of large-data weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some structural assumptions which include ideal gas mixtures. The model is thermodynamically consistent and contains the Maxwell-Stefan

cross-diffusion equations as a special case. Compared to previous works, a very general model class is analyzed, including cross-diffusion effects, temperature gradients, compressible

fluids, and different molar masses. A priori estimates are derived from the entropy balance and the total energy balance. The compactness for the total mass density follows from an improved estimate for the density in L with > 3/2, the effective viscous

flux identity, and uniform bounds related to Feireislīs oscillations defect measure. These bounds rely heavily on the convexity of the free energy and the strong convergence of the relative chemical potentials.

Navier-Stokes-Fourier system, multicomponent fluid, existence of weak solutions, free energy, effective viscous flux identity, oscillations defect measure

http://www.asc.tuwien.ac.at/preprint/2020/asc02x2020.pdf

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