Global solution to the three-dimensional liquid crystal flows of Q-tensor model

TL;DR

This paper establishes the existence of global strong solutions for three-dimensional nematic liquid crystal flows modeled by coupled Navier-Stokes and Q-tensor equations, under certain conditions on energy coefficients.

Contribution

It provides the first proof of global strong solutions for 3D liquid crystal flows with small initial data in the Q-tensor framework.

Findings

Global strong solutions exist for small initial data

Conditions on Landau-de Gennes energy coefficients are identified

The coupled Navier-Stokes and Q-tensor system is well-posed under these conditions

Abstract

A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows. Under suitable condition on the coefficients of the Landau-de Gennes energy functional, global strong solution for small initial data is proved.