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We consider a model of liquid crystals, based on a nonlinear hyperbolicsystem of differential equations, that represents an inviscid version of themodel proposed by Qian and Sheng. A new concept of dissipative solution isproposed, for which a global-in-time existence theorem is shown. Thedissipative solutions enjoy the following properties:  (i) they exist globally in time for any finite energy initial data;  (ii) dissipative solutions enjoying certain smoothness are classicalsolutions;  (iii) a dissipative solution coincides with a strong solution originatingfrom the same initial data as long as the latter exists.

On a hyperbolic system arising in liquid crystals modeling