In this talk, we present some results on three-dimensional nematic liquid crystal flows with the Oseen-Frank energy. On the one hand, ignoring Leslie tensor, we established the well-posedness of Ericksen-Leslie system in uniformly locally L^3-spaces. On the other hand, when the effect of Leslie tensor is considered, we proved the local well-posedness of strong solutions to the Ericksen-Leslie system as well as the smooth convergence of the Ginzburg-Landau approximation once away from initial time. These works are joint with Professor Min-Chun Hong and Mr. Zhewen Feng.
