A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion

<p style='text-indent:20px;'>After the pioneering work by Giovangigli on mathematics of multicomponent flows, several attempts were made to introduce global weak solutions for PDEs describing dynamics fluid mixtures. While incompressible case with constant density was enlighted well enough due results Chen and Jüngel (isothermal case), or Marion Temam, some open questions remain solution theory gas mixtures their corresponding equations mixed parabolic–hyperbolic type. For instance, Mucha, Pokorny Zatorska showed possibility stabilise hyperbolic component means Bresch-Desjardins technique a regularisation pressure preventing vacuum. The result Dreyer, Druet, Gajewski Guhlke avoids <i>ex machina</i> stabilisations, but mathematical assumption that Onsager matrix is uniformly positive certain subspaces leads, in dilute limit, infinite diffusion velocities which are not compatible Maxwell-Stefan form fluxes. In this paper, we prove existence isothermal ideal compressible natural diffusion. main new tool an asymptotic condition imposed at low binary diffusivities, compensates possibly extreme behaviour rarefied regime.</p>