Global existence and optimal time decay rate of the solutions to the incompressible biaxial nematic liquid crystals flows in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^3$$\end{document}

This paper is to investigate global existence and optimal time decay rate of the solutions to the incompressible biaxial nematic liquid crystals flows in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^3$$\end{document}. Firstly, the global existence follows from local existence theory, the uniformly a priori estimate and the continuity argument. Secondly, by using the high- and low-frequency decomposition, we obtain the optimal time decay rates of the velocity and two directors.