On a hyperbolic system arising in liquid crystal modelling
Abstract
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 nite 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.