A representation formula of incompressible liquid crystal flow and its applications. (3rd April 2017)

• Record Type: Journal Article
• Authors: Huang, Xiangdi
• Is Part Of: Nonlinearity. Volume 30:Number 5(2017:May)
• Page Start: 1911
• Page End: 1919
• Publication Date: 2017-04-03
• Subjects: global existence -- liquid crystals -- strong solution; primary 76D05 -- secondary 35Q35; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa63a5
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we give a representation formula for the solutions of incompressible liquid crystal flow in arbitrary dimensions. As a direct application, one can obtain a strong global solution in two dimensions, as long as the image of the initial orientation field of the liquid crystal lies in a plane, or is a nontrivial curve on the unit sphere. The results also hold for inhomogeneous incompressible liquid crystals. This generalizes the results in Gong et al (2015 Nonlinearity 28 3677–94) and Dong and Lei (2012 (arXiv:org/abs/1205.3697)).