  We study a hydrodynamic limit of a system of coupled kinetic and fluid
equations under a strong local alignment force and a strong Brownian motion.
More precisely, we consider the Vlasov-Fokker-Planck type equation and
compressible Navier-Stokes equations with a density-dependent viscosity. Based
on a relative entropy argument, by assuming the existence of weak solutions to
that kinetic-fluid system, we rigorously derive a two-phase fluid model
consisting of isothermal Euler equations and compressible Navier-Stokes
equations with a density-dependent viscosity.
