Global well posedness for a Q-tensor model of nematic liquid crystals

TL;DR

This paper establishes the global existence and decay behavior of solutions for a coupled Navier-Stokes and Q-tensor model describing nematic liquid crystals in higher dimensions, using advanced regularity and decay estimates.

Contribution

It proves the global well-posedness and decay estimates for a Q-tensor model of nematic liquid crystals in rom the linearized problem, employing maximal regularity and decay techniques.

Findings

Global well-posedness in or the model

Decay estimates for solutions over time

Application of maximal regularity methods

Abstract

In this paper, we prove the global well posedness and the decay estimates for a $\mathbb Q$-tensor model of nematic liquid crystals in $\mathbb R^N$, $N \geq 3$. This system is coupled system by the Navier-Stokes equations with a parabolic-type equation describing the evolution of the director fields $\mathbb Q$. The proof is based on the maximal $L_p$ -$L_q$ regularity and the $L_p$ -$L_q$ decay estimates to the linearized problem.