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