  In this paper, we establish the local well-posedness and blow-up criteria of
strong solutions to the Ericksen-Leslie system in $\Bbb R^3$ for the well-known
Oseen-Frank model. The local existence of strong solutions to liquid crystal
flows is obtained by using the Ginzburg-Landau approximation approach to
guarantee the constraint that the direction vector of the fluid is of length
one. We establish four kinds of blow-up criteria, including (i) the Serrin
type; (ii) the Beal-Kato-Majda type; (iii) the mixed type, i.e., Serrin type
condition for one field and Beal-Kato-Majda type condition on the other one;
(iv) a new one, which characterizes the maximal existence time of the strong
solutions to the Ericksen-Leslie system in terms of Serrin type norms of the
strong solutions to the Ginzburg-Landau approximate system. Furthermore, we
also prove that the strong solutions of the Ginzburg-Landau approximate system
converge to the strong solution of the Ericksen-Leslie system up to the maximal
existence time.
