Regularity and Existence of Global Solutions to the Ericksen-leslie System in R

In this paper, we first establish the regularity theorem for suitable weak solutions to the EricksenLeslie system in R2. Building on such a regularity, we then establish the existence of a global weak solution to the Ericksen-Leslie system in R2 for any initial data in the energy space, under the physical constraint conditions on the Leslie coefficients ensuring the dissipation of energy of the system, which is smooth away from at most finitely many times. This extends earlier works by Lin-Lin-Wang [23] on a simplified nematic liquid crystal flow to the general Ericksen-Leslie system.