中文摘要：

该文将证明,即使初始密度在Ω中没有正下界,二维向列液晶流体存在半强解.该文主要的新颖点在于新估计｜｜（a）td｜｜L4/3（I,L2（Ω））不依赖于ρ的下界,其中d及p分别表示流体的密度与分子方向.

英文摘要：

In this paper, we show the existence of semi-strong solutions to hydrodynamic flow of the two-dimensional nematic liquid crystals with small initial data, even though the initial density does not possess the positive lower bound in Ω. The main novelty of the paper lies in the fact that our new estimate of ｜｜（a）td｜｜L4/3（I,L2（Ω）） is independent of the lower-bound of p, where d and p represent the director of the molecules and the density of the fluid, respectively.