DCDS
Globally weak solutions to the flow of compressible liquid crystals system
Xian-Gao Liu Jie Qing
We study a simplified system for the compressible fluid of Nematic Liquid Crystals in a bounded domain in three Euclidean space and prove the global existence of the finite energy weak solutions.
keywords: global existence. compressible Nematic liquid crystals
DCDS
Serrin's regularity results for the incompressible liquid crystals system
Xian-Gao Liu Jianzhong Min Kui Wang Xiaotao Zhang
In this paper, we study the simplified system of the original Ericksen--Leslie equations for the flow of liquid crystals [10]. Under Serrin criteria [13], we prove a partial interior regularity result of weak solutions for the three-dimensional incompressible liquid crystal system.
keywords: partial regularity Serrin criteria heat kernel theory. Incompressible liquid crystals Calderón-Zygmund inequality
CPAA
The existence and blow-up criterion of liquid crystals system in critical Besov space
Yi-hang Hao Xian-Gao Liu
We consider the existence of strong solution to liquid crystals system in critical Besov space, and give a criterion which is similar to Serrin's criterion on regularity of weak solution to Navier-Stokes equations.
keywords: liquid crystals strong solution. Littlewood-Paley theory

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