  We are concerned with the Cauchy problem of the two-dimensional (2D)
nonhomogeneous incompressible nematic liquid crystal flows on the whole space
$\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D
nonhomogeneous incompressible nematic liquid crystal flows admits a unique
global strong solution provided the initial data density and the gradient of
orientation decay not too slow at infinity, and the basic energy
$\|\sqrt{\rho_0}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2$ is
small. In particular, the initial density may contain vacuum states and even
have compact support. Moreover, the large time behavior of the solution is also
obtained.
