  In this paper, we consider a two-phase flow model consisting of the
compressible Navier-Stokes systems with degenerate viscosity coupled with the
compressible Navier-Stokes systems with constant viscosities via a drag force,
which can be derived from Chapman-Enskog expansion for the compressible
Navier-Stokes-Vlasov-Fokker-Planck system. For general initial data, we
establish the global existence of weak solutions with finite energy to the
initial value problem in the three-dimensional periodic domain, and prove the
convergence of global weak solutions to its equilibrium state as the time tends
to infinity.
