  This paper studies global existence, hydrodynamic limit, and large-time
behavior of weak solutions to a kinetic flocking model coupled to the
incompressible Navier-Stokes equations. The model describes the motion of
particles immersed in a Navier-Stokes fluid interacting through local
alignment. We first prove the existence of weak solutions using energy and
$L^p$ estimates together with the velocity averaging lemma. We also rigorously
establish a hydrodynamic limit corresponding to strong noise and local
alignment. In this limit, the dynamics can be totally described by a coupled
compressible Euler - incompressible Navier-Stokes system. The proof is via
relative entropy techniques. Finally, we show a conditional result on the
large-time behavior of classical solutions. Specifically, if the mass-density
satisfies a uniform in time integrability estimate, then particles align with
the fluid velocity exponentially fast without any further assumption on the
viscosity of the fluid.
