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Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures Pokorný, Milan


We present large-data existence result for weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures. General free energies satisfying some structural assumptions are considered, 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 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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