  We investigate in this paper the global stability of the compressible viscous
surface waves in the absence of surface tension effect with a steady-state
violating Rayleigh-Taylor instability and the reference domain being the
horizontal infinite layer. The fluid dynamics are governed by the 3-D
gravity-driven isentropic compressible Navier-Stokes equations. We develop a
mathematical approach to establish global well-posedness of free boundary
problems of the multi-dimensional compressible Navier-Stokes system based on
the Lagrangian framework, which requires no nonlinear compatibility conditions
on the initial data.
