Asymptotic Behavior of Solutions to the Liquid Crystals System in $\mathbb{R}^3$

TL;DR

This paper investigates the long-term behavior of solutions to the nematic liquid crystals system in three-dimensional space, focusing on how solutions evolve over time with small initial disturbances.

Contribution

It provides new insights into the asymptotic behavior of liquid crystal solutions in unbounded domains with small initial data.

Findings

Solutions decay over time at specific rates.

The analysis confirms stability of solutions for small initial data.

Asymptotic profiles of solutions are characterized.

Abstract

In this paper we study the large time behavior of solutions to a nematic liquid crystals system in the whole space $\mathbb{R}^3$. The fluid under consideration has constant density and small initial data.