Weak solutions for the Stokes system for compressible fluids with general pressure

We prove existence and uniqueness of global in time weak solutions for the Stokes system compressible fluids with a general, non-monotone pressure. construct solution at level Lagrangian formulation then define transformation to original Eulerian coordinates. For nonnegative bounded initial density, is all t>0 as well belongs L∞([0,∞)×Td). A key point our considerations such transformation. Since velocity might not be Lipschitz continuous, we develop method which relies on results Crippa & De Lellis, concerning regular flows. The obtained thanks application certain weighted flow detail analysis based properties BMO space.