Recent developments of analysis for hydrodynamic flow of nematic liquid crystals

Abstract

The study of hydrodynamics of liquid crystal leads to many fasci- nating mathematical problems, which has prompted various interesting works recently. This article reviews the static Oseen-Frank theory and surveys some recent progress on the existence, regularity, uniqueness, and large time asymp- totic of the hydrodynamic flow of nematic liquid crystals. We will also propose a few interesting questions for future investigations.

Phil. Trans. R. Soc., A, to appear

References in corpus (3)

• Global Well-Posedness with Large Oscillations and Vacuum to the Three-Dimensional Equations of Compressible Nematic Liquid Crystal Flows
• Global existence of weak solutions of the nematic liquid crystal flow in dimensions three
• The small Deborah number limit of the Doi-Onsager equation to the Ericksen-Leslie equation

Cited by in corpus (7)

• Long-time Behavior of Solution for the Compressible Nematic Liquid Crystal Flows in ${\mathbb{R}}^3$
• On static and hydrodynamic biaxial nematic liquid crystals
• Modeling and Computation of Liquid Crystals
• Twisted solutions to a simplified Ericksen-Leslie equation
• Weak solutions of non-isothermal nematic liquid crystal flow in dimension three
• Asymptotic Behavior of Solution to the Incompressible Nematic Liquid Crystal Flows in R^3
• Rigorous justification of the uniaxial limit from Qian-Sheng's inertial $Q$-tensor theory to the Ericksen-Leslie theory