数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (3): 947-972.doi: 10.1007/s10473-024-0310-0

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THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

Shuang Chen, Shanshan Guo, Qiuju Xu*   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
  • 收稿日期:2022-12-13 修回日期:2023-03-16 出版日期:2024-06-25 发布日期:2024-05-21

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

Shuang Chen, Shanshan Guo, Qiuju Xu*   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
  • Received:2022-12-13 Revised:2023-03-16 Online:2024-06-25 Published:2024-05-21
  • Contact: *Qiuju Xu, smlynice@163.com
  • About author:Shuang Chen, E-mail:chenshuang010877@163.com; Shanshan Guo, guoshanshan0516@163.com
  • Supported by:
    Guo's research was partially supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202100523, KJQN202000536), the National Natural Science Foundation of China (12001074) and the Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0606); Xu's research was supported by the National Natural Science Foundation of Chongqing (CSTB2023NSCQ-MSX0278), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K202100503) and the Research Project of Chongqing Education Commission (CXQT21014).

摘要: In this paper, we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain. Under some smallness and structural assumptions imposed on the time-periodic force, we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory. We also prove a uniqueness result via energy estimates.

关键词: compressible nematic liquid crystals, time-periodic solution, topological degree theory, energy estimates

Abstract: In this paper, we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain. Under some smallness and structural assumptions imposed on the time-periodic force, we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory. We also prove a uniqueness result via energy estimates.

Key words: compressible nematic liquid crystals, time-periodic solution, topological degree theory, energy estimates

中图分类号: 

  • 76A15