On a hyperbolic system arising in liquid crystals modeling
  We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution is proposed, for which a global-in-time existence theorem is shown. The dissipative solutions enjoy the following properties:   (i) they exist globally in time for any finite energy initial data;   (ii) dissipative solutions enjoying certain smoothness are classical solutions;   (iii) a dissipative solution coincides with a strong solution originating from the same initial data as long as the latter exists. 
E. Feireisl, E. Rocca, G. Schimperna, A. Zarnescu
math.AP