  In this paper, we study global existence and large time behaviors of strong
solutions to the kinetic Cucker--Smale model coupled with the three dimensional
incompressible Navier--Stokes equations in the whole space. Using the maximal
regularity estimate on the Stokes equations, global-in-time strong solutions to
the Cauchy problem of the coupled system are obtained under small initial data
regime. The optimal decay rate of the system, in the sense that the energy of
the system decays at a rate coinciding with the one corresponding to the
underling incompressible Navier--Stokes equations without the coupling term, is
also analyzed. Compared with previous results set in spatial-periodic or
bounded domains, we circumvent the difficulty caused by unboundedness of the
domain using the Fourier splitting method.
