Stationary Mixture BGK Models with the Correct Fick Coefficients

Unlike the single species gases, the transport coefficients such as Fick, Soret, Dufour coefficients arise in the hydrodynamic limit of multi-species gas mixtures. To the best of the authors’ knowledge, no multi-component relaxational models is reported that produces all these values correctly. In this paper, we establish the existence of unique stationary mild solutions to the BGK models for gas mixtures which produces the correct Fick coefficients in the Navier–Stokes limit for inert gases (Brull in Eur J Mech B 33:74–86, 2012), and for reactive gases (Brull and Schneider in Commun Math Sci 12(7):1199–1223, 2014) in a unified manner.