| Abstract: |
| The existence of large-data weak solutions to the evolutionary compressible
Navier--Stokes--Fourier system for chemically reacting fluid mixtures is proved.
General free energies are considered satisfying some structural assumptions,
with a pressure containing a $\gamma$-power law.
The model is thermodynamically consistent and contains the Maxwell--Stefan
cross-diffusion equations in the Fick--Onsager form
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 estimate for the
pressure in $L^p$ with $p>1$,
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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