  We study an asymptotic analysis of a coupled system of kinetic and fluid
equations. More precisely, we deal with the nonlinear Vlasov-Fokker-Planck
equation coupled with the compressible isentropic Navier-Stokes system through
a drag force in a bounded domain with the specular reflection boundary
condition for the kinetic equation and homogeneous Dirichlet boundary condition
for the fluid system. We establish a rigorous hydrodynamic limit corresponding
to strong noise and local alignment force. The limiting system is a type of
two-phase fluid model consisting of the isothermal Euler system and the
compressible Navier-Stokes system. Our main strategy relies on the relative
entropy argument based on the weak-strong uniqueness principle. For this, we
provide a global-in-time existence of weak solutions for the coupled
kinetic-fluid system. We also show the existence and uniqueness of strong
solutions to the limiting system in a bounded domain with the kinematic
boundary condition for the Euler system and Dirichlet boundary condition for
the Navier-Stokes system.
