  In this paper, we investigate the Cauchy problem for the incompressible
nematic liquid crystal flows in three-dimensional whole space. First of all, we
establish the global existence of solution by energy method under assumption of
small initial data. Furthermore, the time decay rates of velocity and director
are built when the initial data belongs to $L^1(\mathbb{R}^3)$ additionally.
Finally, one also constructs the time convergence rates for the mixed
space-time derivatives of velocity and director.
