In this paper, we investigate the initial value problem for the three dimensional nematic liquid crystal flows with two directional viscosity. The main purpose of this paper is to establish global well-posedness of classical small solutions. The proof is mainly based on the energy estimate, anisotropic type Sobolev inequality and bootstrapping argument.

中文翻译：

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具有双向粘度的3D向列液晶流的全局经典解决方案

在本文中，我们研究了具有双向粘度的三维向列液晶流的初值问题。本文的主要目的是建立经典小解的全局适定性。证明主要基于能量估计，各向异性类型的Sobolev不等式和自举参数。