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We prove existence of global in time weak solutions to a compressibletwo-fluid Stokes system with a single velocity field and algebraic closure forthe pressure law. The constitutive relation involves densities of both fluidsthrough an implicit function. The system appears to be outside the class ofproblems that can be treated using the classical Lions-Feireisl approach.Adapting the novel compactness tool developed by the first author and P.-E.Jabin in the mono-fluid compressible Navier-Stokes setting, we first prove theweak sequential stability of solutions. Next, we construct weak solutions viaunconventional approximation using the Lagrangian formulation, truncations andstability result of trajectories for rough velocity fields.

Finite-energy solutions for compressible two-fluid Stokes system