Global Low-Energy Weak Solution and Large-Time Behavior for the   Compressible Flow of Liquid Crystals
  We consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in $\mathbb R^3$. When the initial data is small in $L^2$ and initial density is positive and essentially bounded, we first prove the existence of a global weak solution in $\mathbb R^3$. The large-time behavior of a global weak solution is also established. 
Guochun Wu, Zhong Tan
math.AP