Global well-posedness for the dynamical Q-tensor model of liquid crystals

TL;DR

This paper proves the global existence and uniqueness of solutions for a complex liquid crystal model coupling Navier-Stokes and Q-tensor equations, advancing understanding of nematic liquid crystal flows.

Contribution

It establishes the global well-posedness of weak and strong solutions for the coupled system in three dimensions, including continuous dependence on initial data.

Findings

Global existence of weak solutions in 3D

Global well-posedness of strong solutions with large viscosity

Weak-strong uniqueness of solutions

Abstract

In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.