  We study the global existence of a unique strong solution and its large-time
behavior of a two-phase fluid system consisting of the compressible isothermal
Euler equations coupled with compressible isentropic Navier-Stokes equations
through a drag forcing term. The coupled system can be derived as the
hydrodynamic limit of the Vlasov-Fokker-Planck/isentropic Navier-Stokes
equations with strong local alignment forces. When the initial data is
sufficiently small and regular, we establish the unique existence of the global
$H^s$-solutions in a perturbation framework. We also provide the large-time
behavior of classical solutions showing the alignment between two fluid
velocities exponentially fast as time evolves. For this, we construct a
Lyapunov function measuring the fluctuations of momentum and mass from its
averaged quantities.
