  In this paper, we consider the Cauchy problem of the incompressible liquid
crystal equations in $n$ dimensions. We prove the local well-posedness of mild
solutions to the liquid crystal equations with $L^\infty$ initial data, in
particular, the initial energy may be infinite. We prove that the solutions are
smooth with respect to the space variables away from the initial time. Based on
this regularity estimate, we employ the blow up argument and Liouville type
theorems to establish vorticity direction type blow up criterions for the type
I mild solutions established in the present paper.
