  This paper concerns the uniqueness of weak solutions to the Cauchy problem to
the Ericksen-Leslie system of liquid crystal models in $\mathbb R^2$, with both
general Leslie stress tensors and general Oseen-Frank density. It is shown here
that such a system admits a unique weak solution provided that the Frank
coefficients are close to some positive constant, which solves an interesting
open problem. One of the main ideas of our proof is to perform suitable energy
estimates at level one order lower than the natural basic energy estimates for
the Ericksen-Leslie system.
