Global existence of the finite energy weak solutions to a nematic liquid crystals model

摘要

In this paper, we are concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. For a bounded domain in ?3, under the assumption that initial density belongs to, we show the global existence of weak solutions to the nematic liquid crystals model with a penalized system. Furthermore, we also obtain the energy inequality for weak solutions.