  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.
