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
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  • School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
Shuang Chen, E-mail:chenshuang010877@163.com; Shanshan Guo, guoshanshan0516@163.com

Received date: 2022-12-13

  Revised date: 2023-03-16

  Online published: 2024-05-21

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).

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.

Cite this article

Shuang Chen , Shanshan Guo , Qiuju Xu . THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN[J]. Acta mathematica scientia, Series B, 2024 , 44(3) : 947 -972 . DOI: 10.1007/s10473-024-0310-0

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