  We prove existence of globally bounded weak solutions to the compressible
Stokes system with a general non-monotone pressure term. It turns out that the
solution is unique for a bounded initial density. From the Lagrangian
formulation of the system, we first obtain the $L^\infty$ bounds and then
construct the solution in Eulerian coordinates using the tools from the theory
of transport equations. The velocity might not be Lipschitz continuous, however
its gradient belongs to $L^\infty([0,\infty);BMO)$ and the uniqueness is shown
using the key properties of the $BMO$ space.
