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.
On a hyperbolic system arising in liquid crystals modeling
ROCCA, ELISABETTA;SCHIMPERNA, GIULIO FERNANDO;
2018-01-01
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 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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
