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Global Existence of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Compressible Nematic Liquid Crystal Flows

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Abstract

This paper is concerned with a simplified hydrodynamic flow modeling the three-dimensional motion of compressible, nematic liquid crystal materials. The authors establish the global existence of classical solution to the Cauchy problem with smooth initial data which are of small energy but possibly large oscillations with constant state as far-field condition which could be either vacuum or non-vacuum. The initial density is allowed to vanish and the spatial measure of the set of vacuum can be arbitrarily large, in particular, the initial density can even have compact support. As a byproduct, the large-time behavior of the solution is also studied.

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Acknowledgements

The authors are indebted to the referees for the useful suggestions which improve the presentation of this paper. This work is partially supported by NNSFC (Grant Nos. 11671333, 11271306), the Natural Science Foundation of Fujian Province of China (Grant No. 2015J01023), and the Fundamental Research Funds for the Central Universities (Grant No. 20720160012).

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Authors and Affiliations

  1. Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, Hong Kong

    Jinkai Li

  2. College of Science, Northeast Dianli University, Jilin, 132013, People’s Republic of China

    Zhonghai Xu

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

    Jianwen Zhang

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  1. Jinkai Li
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  2. Zhonghai Xu
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  3. Jianwen Zhang
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Correspondence to Jianwen Zhang.

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The authors declare that they have no conflict of interest.

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Communicated by G.-Q. Chen.

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Li, J., Xu, Z. & Zhang, J. Global Existence of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Compressible Nematic Liquid Crystal Flows. J. Math. Fluid Mech. 20, 2105–2145 (2018). https://doi.org/10.1007/s00021-018-0400-7

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  • DOI: https://doi.org/10.1007/s00021-018-0400-7

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