Global finite energy weak solutions to the compressible nematic liquid   crystal flow in dimension three
  In this paper, we consider the initial and boundary value problem of a simplified compressible nematic liquid crystal flow in $\Omega\subset\mathbb R^3$. We establish the existence of global weak solutions, provided the initial orientational director field $d_0$ lies in the hemisphere $\mathbb S^2_+$. 
Junyu Lin, Baishun Lai, and Changyou Wang
math.AP