On well-posedness of Ericksen-Leslie's hyperbolic incompressible liquid crystal model
Analysis of PDEs
2020-07-28 v3
Abstract
We study the Ericksen-Leslie's hyperbolic incompressible liquid crystal model. Under some constraints on the Leslie coefficients which ensure the basic energy law is dissipative, we prove the local-in-time existence and uniqueness of the classical solution to the system with finite initial energy. Furthermore, with an additional assumption on the coefficients which provides a damping effect, and the smallness of the initial energy, the unique global classical solution can be established.
Keywords
Cite
@article{arxiv.1709.06370,
title = {On well-posedness of Ericksen-Leslie's hyperbolic incompressible liquid crystal model},
author = {Ning Jiang and Yi-Long Luo},
journal= {arXiv preprint arXiv:1709.06370},
year = {2020}
}
Comments
This paper supercedes arXiv:1612.04616; 30 pages; some modifications to specially treat the case $\lambda_1 = 0$. arXiv admin note: text overlap with arXiv:1105.2180 by other authors