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.