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Global Well-posedness for the Density-Dependent Incompressible Flow of Liquid Crystals

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Abstract

In the present paper, we consider the global well-posedness of the density-dependent incompressible flow of liquid crystals in \(\mathbb{R}^{2}\). The local existence and uniqueness of the system are obtained without the assumption of small density variation. The global well-posedness is proved when the initial density and liquid crystal orientation are small. However, the initial velocity field is allowed to be arbitrarily large.

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Acknowledgement

This work is supported by NSFC under grant numbers 11601533 and 11571240.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Xiaoping Zhai & Zhi-Min Chen

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  1. Xiaoping Zhai
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  2. Zhi-Min Chen
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Correspondence to Zhi-Min Chen.

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Zhai, X., Chen, ZM. Global Well-posedness for the Density-Dependent Incompressible Flow of Liquid Crystals. Acta Appl Math 158, 139–166 (2018). https://doi.org/10.1007/s10440-018-0178-x

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  • DOI: https://doi.org/10.1007/s10440-018-0178-x

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