| Abstract: |
| We consider a steady flow of heat conducting chemically reacting mixtures in dimension two and three. We focus on both compressible and incompressible setting whose thermodynamics is described by general free energies are considered satisfying some fundamental structural assumptions. We discuss the conditions leading to the existence of weak solution. It is noticeable that the considered models are thermodynamically consistent on one hand and are able to cover the classical models like the Maxwell-Stefan cross-diffusion equations in the Fick-Onsager form as a special case on the other hand. Compared to previous works, a very general model class is analysed, including cross-diffusion effects, temperature gradients, compressible fluids, and different molar masses (in case of compressible fluid). In addition, the technique leading to the compactness of the pressure is a nontrivial generalisation of the use Feireisl`s oscillation defect measure and the newly developed technique relies heavily on the convexity of the free energy and the strong convergence of the relative chemical potentials. |
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