Time decay rate of global strong solutions to nematic liquid crystal flows in $\mathbb R^3_+$

TL;DR

This paper establishes optimal decay rates over time for global strong solutions to nematic liquid crystal flows in three-dimensional half-space, under small initial data conditions in specific Lebesgue spaces.

Contribution

It provides the first optimal decay rate results for these flows in a half-space setting with small initial data.

Findings

Optimal decay rates in $L^r$ spaces for solutions

Decay rates depend on initial data in $L^3$ norm

Results applicable to three-dimensional half-space domain

Abstract

In this paper, we obtain optimal time-decay rates in $L^r(\mathbb R^3_+)$ for $r\ge 1$ of global strong solutions to the nematic liquid crystal flows in $\mathbb R^3_+$, provided the initial data has small $L^3(\mathbb R^3_+)$-norm.