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

  • Xiaoping Zhai
  • Zhi-Min Chen
Article
  • 55 Downloads

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.

Keywords

Global well-posedness Liquid crystal flow Besov space 

Mathematics Subject Classification (2010)

35Q35 35Q30 76D03 

Notes

Acknowledgement

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

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsShenzhen UniversityShenzhenChina

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