The Ericksen-Leslie system for the Oseen-Frank model in liquid crystals

In this talk, I discuss the Ericksen-Leslie system for the Oseen-Frank model with unequal Frank elastic constants in $\mathbb R^3$. In particular, I discuss my new joint work with Dr Mei Yu on the Ericksen-Leslie system in liquid crystal. We prove existence of solutions to the Ericksen-Leslie system with initial data having small local $L^3$-norm. Moreover, we find a new way to remove the restriction on the Frank elastic constants to prove uniqueness of solutions, by using the rotation invariant property of the Oseen-Frank density.