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

Asymptotic analysis for Vlasov-Fokker-Planck/compressible Navier-Stokes equations with a density-dependent viscosity