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

TL;DR

This paper investigates the mathematical well-posedness of a hyperbolic liquid crystal model, proving local and global existence and uniqueness of solutions under certain energy and coefficient conditions.

Contribution

It establishes the local and global well-posedness of the Ericksen-Leslie hyperbolic liquid crystal model with energy dissipation and damping assumptions.

Findings

Local-in-time existence and uniqueness of classical solutions.

Global classical solutions under small initial energy and damping conditions.

Energy law is dissipative under specified Leslie coefficient constraints.

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.