Regularity of Solutions to the Liquid Crystals Systems in $\mathbb{R}^2$   and $\mathbb{R}^3$
  Global existence for weak solutions to systems of nematic liquid crystals, with non-constant fluid density has been established by several authors. In this paper, we establish the regularity and uniqueness results for solutions to the density dependent nematic liquid crystals system. 
Mimi Dai, Jie Qing, Maria E. Schonbek
math.AP