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Global well-posedness to the Cauchy problem of 2D compressible nematic liquid crystal flows with large initial data and vacuum

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Abstract

We study compressible nematic liquid crystal flows with the bulk viscosity being a power function of the density (\(\lambda =\rho ^\beta \)) on the whole two-dimensional (2D) plane. Under a geometric angle condition for the initial direction field, we show the global existence and uniqueness of strong solutions provided that \(\beta >\frac{4}{3}\). It should be noticed that there is no other restrictions on the size of initial data and the initial density allows vacuum states.

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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

    Xin Zhong & Xuan Zhou

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  1. 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 (No. 12371227).

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Zhong, X., Zhou, X. Global well-posedness to the Cauchy problem of 2D compressible nematic liquid crystal flows with large initial data and vacuum. Math. Ann. (2024). https://doi.org/10.1007/s00208-023-02794-5

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  • DOI: https://doi.org/10.1007/s00208-023-02794-5

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