On well-posedness of Ericksen-Leslie's hyperbolic incompressible liquid crystal model

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.

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

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