  In this paper we consider the 2D Ericksen-Leslie equations which describes
the hydrodynamics of nematic Liquid crystal with external body forces and
anisotropic energy modeling the energy of applied external control such as
magnetic or electric field. Under general assumptions on the initial data, the
external data and the anisotropic energy, we prove the existence and uniqueness
of global weak solutions with finitely many singular times. If the initial data
and the external forces are sufficiently small, then we establish that the
global weak solution does not have any singular times and is regular as long as
the data are regular.
