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

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.

29 pages