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Global Classical Solutions to the Compressible Non-isothermal Biaxial Nematic Liquid Crystal Flows with Large Oscillations and Vacuum in 3D Exterior Domains

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Abstract

The compressible non-isothermal biaxial nematic liquid crystal flow is a strongly coupled system between the full compressible Navier–Stokes system and the transported heat flows with two orientation fields. In this paper, we obtain the global existence and large-time behavior of classical solutions to the 3D exterior problem for such a model when the initial total energy is sufficiently small. The assumption on the initial data does not exclude that the initial density may vanish (i.e., vacuum states) in some regions and that it can be of a nontrivially compact support. Our result may be regarded as an extension of Guo–Xi–Xie (J Differ Equ 262(3):1413–1460, 2017) and Li–Tao (Commun Math Sci 21(6):1455–1486, 2023) to the exterior problem of biaxial flows. Some new techniques are developed in order to deal with surface integrals caused by the boundary condition.

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Acknowledgements

The authors would like to express their gratitude to the reviewers for careful reading and helpful suggestions which led to an improvement of the original manuscript.

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Authors and Affiliations

  1. Research Institute for Scientific and Technological Innovation, Changchun Normal University, Changchun, 130032, People’s Republic of China

    Yang Liu

  2. College of Mathematics, Changchun Normal University, Changchun, 130032, People’s Republic of China

    Yang Liu

  3. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Fuguo Wang & Xin Zhong

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The authors claim that the research was realized in collaboration with the same responsibility. All authors read and approved the last version of the manuscript.

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Correspondence to Xin Zhong.

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Communicated by François Gay-Balmaz.

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Liu’s research was partially supported by National Natural Science Foundation of China (No. 12371227), Scientific Research Foundation of Jilin Provincial Education Department (No. JJKH20251032KJ), and Natural Science Foundation of Changchun Normal University (No. CSJJ2024003GZR). Wang’s research was partially supported by Postgraduate Research an Innovation Project of Chongqing (No. CYS23182). Zhong’s research was partially supported by Fundamental Research Funds for the Central Universities (No. SWU–KU24001) and National Natural Science Foundation of China (No. 12371227).

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Liu, Y., Wang, F. & Zhong, X. Global Classical Solutions to the Compressible Non-isothermal Biaxial Nematic Liquid Crystal Flows with Large Oscillations and Vacuum in 3D Exterior Domains. J Nonlinear Sci 35, 40 (2025). https://doi.org/10.1007/s00332-025-10138-7

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