  In the first part of this paper, we establish global existence of solutions
of the liquid crystal (gradient) flow for the well-known Oseen-Frank model. The
liquid crystal flow is a prototype of equations from the Ericksen-Leslie system
in the hydrodynamic theory and generalizes the heat flow for harmonic maps into
the 2-sphere. The Ericksen-Leslie system is a system of the Navier-Stokes
equations coupled with the liquid crystal flow. In the second part of this
paper, we also prove global existence of solutions of the Ericksen-Leslie
system for a general Oseen-Frank model in $\Bbb R^2$.
