Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals

TL;DR

This paper establishes the global well-posedness of the inertial Qian-Sheng liquid crystal model and constructs special twist-wave solutions where the fluid flow remains zero over time.

Contribution

It proves global existence and uniqueness of solutions for the model and introduces twist-wave solutions with zero flow, advancing understanding of liquid crystal dynamics.

Findings

Proved global well-posedness of the inertial Qian-Sheng model.

Constructed explicit twist-wave solutions with zero flow.

Analyzed the energy law governing the system.

Abstract

We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law and prove a global well-posedness result. We further provide an example of twist-wave solutions, that is solutions of the coupled system for which the flow vanishes for all times.