|Existence results in large for fully non-linear compressible multi-fluid models are in the mathematical literature
in a short supply (if not inexisting). In this talk, we shall recall the main ideas of the Lions proof of existence of weak solutions
to the compressible (mono-fluid) Navier-Stokes equations in barotropic regime. We shall then explain how this approach
can be adapted to the construction of weak solutions to some simple multi-fluid models. The main tools
in the proofs are the renormalization techniques for the continuity and transport equations. They will be handled
in more details.