Global existence and optimal time decay rate of the solutions to the incompressible biaxial nematic liquid crystals flows in \(\mathbb {R}^3\)

This paper is to investigate global existence and optimal time decay rate of the solutions to the incompressible biaxial nematic liquid crystals flows in \(\mathbb {R}^3\) ${\mathbb{R}}^3$ . 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.