Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (1): 174-186.doi: 10.1016/S0252-9602(16)30123-0

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ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE COMPRESSIBLE NEMATIC LIQUID CRYSTAL SYSTEM IN R3

Yin LI1,2, Ruiying WEI1,3, Zhengan YAO4   

  1. 1. School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China;
    2. School of Mathematics and Statistics, Yunnan University, Kunming 650091, China;
    3. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2015-09-24 Revised:2016-05-16 Online:2017-02-25 Published:2017-02-25
  • Contact: Ruiying WEI,E-mail:weiruiying521@163.com E-mail:weiruiying521@163.com
  • About author:Yin Lim,E-mail:liyin2009521@163.com;Zhengan YAO,E-mail:mcsyao@mail.sysu.edu.cn
  • Supported by:

    This work is partially supported by NNSFC (11271381 and 11501373), China 973 Program (2011CB808002); the Natural Science Foundation of Guangdong Province (2016A0300310019 and 2016A030307042), Guangdong Provincial culture of seedling of China (2013LYM0081), the Education research platform project of Guangdong Province (2014KQNCX208), the Education Reform Project of Guangdong Province (2015558), the Shaoguan Science and Technology Foundation (20157201), Education Reform Project of Shaoguan University (SYJY20121361 and SYJY20141576).

Abstract:

In this paper, we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1(R3) additionally.

Key words: nematic liquid crystals, decay rates, spectral analysis

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