We consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incompressible Navier–Stokes equations for the fluid velocity. We prove the existence and uniqueness of local in time strong solutions to the system with the initial data near uniaxial equilibrium. The proof is mainly based on the classical Friedrich method to construct approximate solutions and the closed energy estimate.

中文翻译：

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单轴平衡附近惯性钱生Q-张量动力学模型的局部适定性

我们考虑了向列型液晶流的惯性Qian-Sheng Q-张量动力学模型，该模型可以看作一个将Q-张量参数的双曲型方程与不可压缩的Navier-Stokes方程耦合的系统。我们用接近单轴平衡的初始数据证明了该系统在时间上强解的局部性的存在和唯一性。该证明主要基于经典的Friedrich方法构造近似解和封闭能量估计。