Decay for the equations of compressible flow of nematic liquid crystals. (September 2021)

• Record Type: Journal Article
• Authors: Xiong, Jing; Wang, Jialiang; Wang, Weiwei
• Is Part Of: Nonlinear analysis. Volume 210(2021)
• Publication Date: 2021-09
• Subjects: Cauchy problem -- Liquid crystals -- Large-time behavior -- Optimal decay rate; 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.2021.112385
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: It is well-known that the Cauchy problem of the compressible liquid crystals flow admits a unique global-in-time solution, belonging to C 0 ( R 0 +, H l ( R 3 ) ) with l ⩾ 3 ; moreover the lower-order or higher-order derivative of solution enjoys the same decay-in-time rate as well as the linear solution (i.e., the solution of the corresponding linear problem). In this paper we further prove that highest-order derivative of the unique solution also enjoys the same decay-in-time rate as well as the linear solution by developing new analytical skills. In other words, the optimal decay rate for the highest-order derivative of solution can be also obtained.