Time‐periodic solution to the compressible nematic liquid crystal flows in periodic domain. (14th September 2017)

• Record Type: Journal Article
• Authors: Yang, Ying; Tao, Qiang
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 1(2018)
• Page Start: 28
• Page End: 45
• Publication Date: 2017-09-14
• Subjects: energy method -- nematic liquid crystal flows -- time‐periodic solution -- topology degree theory; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4592
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we consider the time‐periodic solution to a simplified version of Ericksen‐Leslie equations modeling the compressible hydrodynamic flow of nematic liquid crystals with a time‐periodic external force in a periodic domain in R N . By using an approach of parabolic regularization and combining with the topology degree theory, we establish the existence of the time‐periodic solution to the model under some smallness and symmetry assumptions on the external force. Then, we give the uniqueness of the periodic solution of this model.