  This paper concerns 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 initial orientation
satisfies a geometric condition (see \eqref{eq1.3}). In particular, the initial
data can be arbitrarily large and the initial density may contain vacuum states
and even have compact support. As a byproduct, the large time behavior of the
solution is also obtained.
