Boudin, Laurent; Grec, Bérénice; Pavić, Milana; Salvarani, Francesco Diffusion asymptotics of a kinetic model for gaseous mixtures. (English) Zbl 1260.35100 Kinet. Relat. Models 6, No. 1, 137-157 (2013). Summary: In this work, we consider the non-reactive fully elastic Boltzmann equations for mixtures in the diffusive scaling. We mainly use a Hilbert expansion of the distribution functions. After briefly recalling the H-theorem, the lower-order non trivial equality obtained from the Boltzmann equations leads to a linear functional equation in the velocity variable. This equation is solved thanks to the Fredholm alternative. Since we consider multicomponent mixtures, the classical techniques introduced by H. Grad [Phys. Fluids 6, 147–181 (1963; Zbl 0115.45006)] cannot be applied, and we propose a new method to treat the terms involving particles with different masses. Cited in 28 Documents MSC: 35Q20 Boltzmann equations 45B05 Fredholm integral equations 35Q35 PDEs in connection with fluid mechanics 82C40 Kinetic theory of gases in time-dependent statistical mechanics Keywords:Boltzmann equations; Fredholm’s alternative; Chapman-Enskog expansion; diffusive scaling; multispecies mixture Citations:Zbl 0115.45006 PDFBibTeX XMLCite \textit{L. Boudin} et al., Kinet. Relat. Models 6, No. 1, 137--157 (2013; Zbl 1260.35100) Full Text: DOI