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

On the 2D Ericksen-Leslie equations with anisotropic energy and external forces