三维非等温可压缩向列型液晶流的Serrin准则

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1058-1076.

三维非等温可压缩向列型液晶流的Serrin准则

寿晓华(),钟新^*()

西南大学数学与统计学院重庆 400715

收稿日期:2024-10-21 修回日期:2025-04-16 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: *E-mail:xzhong1014@amss.ac.cn
作者简介:E-mail:shouxh23@163.com
基金资助:
国家自然科学基金(12371227);重庆市研究生科研创新项目(CYS240128);中央高校基本科研业务费(SWU-KU24001)

A Serrin Criterion for Three-Dimensional Compressible Non-Isothermal Nematic Liquid Crystal Flows

Shou Xiaohua(),Zhong Xin^*()

School of Mathematics and Statistics, Southwest University, Chongqing 400715

Received:2024-10-21 Revised:2025-04-16 Online:2025-08-26 Published:2025-08-01
Supported by:
NSFC(12371227);Postgraduate Research an Innovation Project of Chongqing(CYS240128);Fundamental Research Funds for the Central Universities(SWU-KU24001)

摘要/Abstract

摘要： 该文为三维空间中含真空的可压缩非等温向列型液晶流的柯西问题建立了一个爆破准则. 通过一些精细的分析, 该文深入探究了所研究系统在强耦合与交互作用影响下呈现的结构特性. 结果表明, 如果密度具有上界, 并且速度以及指向场的梯度满足 Serrin 条件, 那么强解是全局存在的. 特别地, 文中建立的 Serrin 准则与温度无关, 并且它与等熵情形下的准则 (Math Methods Appl Sci, 2013, 36: 1363-1375) 完全相同.

关键词: 可压缩非等温液晶流, Serrin 型准则, 真空

Abstract:

We establish a blow-up criterion for the Cauchy problem of compressible non-isothermal nematic liquid crystal flows with vacuum in $\mathbb{R}^3$. It is shown that the strong solution exists globally if the density is bounded from above and the velocity and the gradient of orientation field satisfy the Serrin condition. In particular, our criterion is independent of the temperature and is just the same as that of the isentropic case (Math MethodsAppl Sci, 2013, 36: 1363-1375). This paper presents some delicate analysis to exploit the structural characteristic of the system under consideration due to strong coupling and interplay interaction.

Key words: compressible non-isothermal nematic liquid crystal flows, Serrin criterion, vacuum

中图分类号:

O175.27

寿晓华, 钟新. 三维非等温可压缩向列型液晶流的Serrin准则[J]. 数学物理学报, 2025, 45(4): 1058-1076.

Shou Xiaohua, Zhong Xin. A Serrin Criterion for Three-Dimensional Compressible Non-Isothermal Nematic Liquid Crystal Flows[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1058-1076.

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