Recent developments of analysis for hydrodynamic flow of nematic liquid crystals

TL;DR

This paper reviews recent mathematical progress in understanding the hydrodynamic flow of nematic liquid crystals, focusing on existence, regularity, and asymptotic behavior, and discusses open questions for future research.

Contribution

It surveys recent advances in the mathematical analysis of nematic liquid crystal hydrodynamics, highlighting key results and proposing future research directions.

Findings

Progress on existence, regularity, and uniqueness results

Analysis of large time asymptotic behavior

Identification of open problems for future study

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.