  In this paper we construct a family of exact strong solutions to the
two-dimensional incompressible liquid crystal equations with finite energy. The
initial velocity is chosen to be rotationally symmetric and the image of the
initial orientation of the liquid crystal is a non-trivial curve on the unit
sphere. It turns out that this family of initial data evolves globally in time
by liquid crystal flow and may shrink to a single point as time goes to
infinity.
