The global well-posedness of the Cauchy problem for a liquid crystal system

ABSTRACT

This paper concerns the existence and asymptotic behavior for a system modeling the nematic liquid crystal flow, which consists of a subsystem of compressible Navier–Stokes equations coupling with heat flow for harmonic mapping. Under some assumptions on initial data, we established global existence and asymptotic behavior of solutions in of the Cauchy problem for liquid crystal equations.

Keywords:

• Liquid crystal system
• Cauchy problem
• global existence
• Ericksen–Leslie system
• Navier–Stokes equations

AMS Subject Classifications:

• 35Q30
• 35B40
• 35B41
• 76D03
• 76D05

Acknowledgements

The authors thank the referees by his/her comments, which led to improvements in the presentation of this paper. Moreover, the authors express their sincere thanks to Dr Xinguang Yang for his suggestion for this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper is partly support by the NSFC of China [grant number 11501199].