On a hyperbolic system arising in liquid crystals modeling
Analysis of PDEs
2016-10-26 v1
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.
Keywords
Cite
@article{arxiv.1610.07828,
title = {On a hyperbolic system arising in liquid crystals modeling},
author = {E. Feireisl and E. Rocca and G. Schimperna and A. Zarnescu},
journal= {arXiv preprint arXiv:1610.07828},
year = {2016}
}