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<p>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.</p>

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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

  • 期刊论文

  • 发表日期：

    2025年2月11日

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  • Yang Liu,
  • Fuguo Wang,
  • Xin Zhong

摘要

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.