Global solution to the 3-D density-dependent incompressible flow of liquid crystals. (June 2017)

• Record Type: Journal Article
• Authors: Zhai, Xiaoping; Li, Yongsheng; Yan, Wei
• Is Part Of: Nonlinear analysis. Volume 156(2017)
• Page Start: 249
• Page End: 274
• Publication Date: 2017-06
• Subjects: Global well-posedness -- Liquid crystal flows -- Besov space; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.02.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the global wellposedness of the 3-D density-dependent incompressible flow of liquid crystals in the critical Besov spaces. We first get the local solution for this system without assumptions of small density variation and then extend this local solution to be global under the smallness assumptions on initial density, initial orientation field and the horizontal components of the initial velocity field. This result implies the global well-posedness of this system with large initial vertical velocity component.