Well-posedness of the fractional Ginzburg–Landau equation

ABSTRACT

In this paper, we investigate the well-posedness of the real fractional Ginzburg–Landau equation in several different function spaces, which have been used to deal with the Burgers’ equation, the semilinear heat equation, the Navier–Stokes equations, etc. The long time asymptotic behavior of the nonnegative global solutions is also studied in details.

KEYWORDS:

• Fractional Ginzburg–Landau equation
• Well-posedness
• Sobolev space
• Asymptotic behavior

AMS SUBJECT CLASSIFICATIONS:

• 35K55
• 35Q92
• 35Q35
• 92C17

Acknowledgements

The authors would like to thank the anonymous referees and the editor Prof. Yongzhi Steve Xu for their helpful comments that improved the presentation of this paper. The authors are also grateful to Prof. Ting-Zhu Huang and Prof. Zhao-Yin Xiang for carefully reading earlier version of the current paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by NSFC [grant number 61702083], [grant number 11501085], [grant number 11701467], [grant number 11701475], [grant number 11601365]; the Fundamental Research Funds for the Central Universities [grant number ZYGX2016J132], [grant number ZYGX2016J138], [grant number 2682017CX068].