  In this paper, we consider the Cauchy problem to the Ericksen-Leslie system
of liquid crystals in $\mathbb R^3$. Global well-posedness of strong solutions
are obtained under the condition that the product of $\|u_0\|_2+\|\nabla
d_0\|_2$ and $\|\nabla u_0\|_2+\|\nabla^2d_0\|_2$ is suitably small. This
result can be viewed as a supplement to the local existence and blow up
criteria discussed in \cite{Hong1}.
