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Global Existence and the Optimal Decay Rates for the Three Dimensional Compressible Nematic Liquid Crystal Flow

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Abstract

The present paper is dedicated to the study of the Cauchy problems for the three-dimensional compressible nematic liquid crystal flow. We obtain the global existence and the optimal decay rates of smooth solutions to the system under the condition that the initial data in lower regular spaces are close to the constant equilibrium state. Our main method is based on the spectral analysis and the smooth effect of dissipative operator.

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Authors and Affiliations

  1. School of Science, Shandong University of Technology, Zibo, 255049, Shandong, China

    Fuyi Xu

  2. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, 100038, China

    Fuyi Xu

  3. School of Mathematical Sciences, Yantai University, Yantai, 264005, Shandong, China

    Xinguang Zhang

  4. Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia

    Xinguang Zhang, Yonghong Wu & Lishan Liu

Authors
  1. Fuyi Xu
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  2. Xinguang Zhang
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  3. Yonghong Wu
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  4. Lishan Liu
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Corresponding author

Correspondence to Fuyi Xu.

Additional information

Research supported by the National Natural Science Foundation of China (11501332, 11171034, 11371221), the Natural Science Foundation of Shandong Province (ZR2015AL007), China Postdoctoral Science Foundation funded project (2014M561893), Postdoctoral innovation fund of Shandong Province, the Open Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research Fund (IWHR-SKL-201407), and the Specialized Research Foundation for the Doctoral Program of Higher Education of China (20123705110001), and Young Scholars Research Fund of Shandong University of Technology.

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Xu, F., Zhang, X., Wu, Y. et al. Global Existence and the Optimal Decay Rates for the Three Dimensional Compressible Nematic Liquid Crystal Flow. Acta Appl Math 150, 67–80 (2017). https://doi.org/10.1007/s10440-017-0094-5

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  • DOI: https://doi.org/10.1007/s10440-017-0094-5

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