WEAK SOLUTIONS FOR A BIFLUID MODEL FOR A MIXTURE OF TWO COMPRESSIBLE NONINTERACTING FLUIDS WITH GENERAL BOUNDARY DATA

We prove global existence of weak solutions for a version of the one velocity Baer-Nunziato system with dissipation describing a mixture of two noninteracting viscous compressible fluids in a piecewise regular Lipschitz domain with general inflow/outflow boundary conditions. The geometrical setting is general enough to comply with most current domains important for applications, such as (curved) pipes of piecewise regular and axis-dependent cross-sections. For the existence proof, we adapt to the system the classical Lions-Feireisl approach to the compressible Navier-Stokes equations which is combined with a generalization of the theory of renormalized solutions to the transport equations in the spirit of Vasseur, Wen, and Yu [J. Math. Pures Appl. (9), 125 (2019), pp. 247-282]. The results related to the families of transport equations presented in this paper extend/improve some statements of the theory of renormalized solutions and are therefore of independent interest.