# American Institute of Mathematical Sciences

July  2020, 40(7): 4479-4496. doi: 10.3934/dcds.2020187

## Global well-posedness to incompressible non-inertial Qian-Sheng model

 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

* Corresponding author: Yangjun Ma

Received  September 2019 Published  April 2020

Fund Project: This work is supported by the grants from the National Natural Foundation of China under contract No. 11971360

In this paper we study the incompressible non-inertial Qian-Sheng model, which describes the hydrodynamics of nematic liquid crystals without inertial effect in the $Q$-tensor framework. Under some proper assumptions on the viscous coefficients, we prove the local well-posedness with large initial data and the global existence with small size of the initial data in the classical solutions regime.

Citation: Yangjun Ma. Global well-posedness to incompressible non-inertial Qian-Sheng model. Discrete & Continuous Dynamical Systems, 2020, 40 (7) : 4479-4496. doi: 10.3934/dcds.2020187
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