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