三维非等温可压缩向列型液晶流的Serrin准则

Abstract

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

CLC Number:

O175.27

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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References 25

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

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