  This paper concerns the dynamics of two layers of compressible, barotropic,
viscous fluid lying atop one another. The lower fluid is bounded below by a
rigid bottom, and the upper fluid is bounded above by a trivial fluid of
constant pressure. This is a free boundary problem: the interfaces between the
fluids and above the upper fluid are free to move. The fluids are acted on by
gravity in the bulk, and at the free interfaces we consider both the case of
surface tension and the case of no surface forces. We are concerned with the
Rayleigh-Taylor instability when the upper fluid is heavier than the lower
fluid along the equilibrium interface. When the surface tension at the free
internal interface is below the critical value, we prove that the problem is
nonlinear unstable.
