| Abstract: |
| 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 $L^{\gamma}$ with $\gamma>3/2$, the effective viscous
flux identity, and uniform bounds related to Feireisl`s oscillations defect measure.
These bounds rely heavily on the convexity of the free energy and the strong convergence
of the relative chemical potentials. |
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