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Global Strong Solutions to the Compressible Nematic Liquid Crystal Flows with Large Oscillations and Vacuum in 2D Bounded Domains

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Abstract

We investigate a simplified compressible nematic liquid crystal flow in two-dimensional (2D) bounded domains with Navier slip boundary conditions for velocity and Neumann boundary condition for orientation field. Based on delicate energy method and the structure of the model under consideration, we show the global existence and uniqueness of strong solutions when the initial total energy is suitably small. Our result may be regarded as an extension of the 2D Cauchy problem due to Wang (J Math Fluid Mech 18(3):539–569, 2016).

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

    Yimin Sun & Xin Zhong

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  1. Yimin Sun
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  2. Xin Zhong
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Correspondence to Xin Zhong.

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This research was partially supported by National Natural Science Foundation of China (Nos. 11901474, 12071359).

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Sun, Y., Zhong, X. Global Strong Solutions to the Compressible Nematic Liquid Crystal Flows with Large Oscillations and Vacuum in 2D Bounded Domains. J Geom Anal 33, 319 (2023). https://doi.org/10.1007/s12220-023-01386-8

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