Global well-posedness of weak and strong solutions to the nD phase-lock system

Abstract

In this paper, we prove the global well-posedness of weak and strong solutions to the $nD(n\ge 3)$ phase-lock system under the Coulomb gauge.

COMMUNICATED BY:

• Meir Shillor

Keywords:

• Well-posedness
• weak solutions
• strong solutions
• Coulomb gauge

2010 Mathematics Subject Classifications:

• 35A05
• 35A40
• 35K55
• 82D55

Acknowledgments

The authors thank the referee for careful reading and helpful suggestions. This work is partially supported by National Natural Science Foundation of China (NSFC) (Nos. 11971234 and 71772153) and Fundamental Research Funds for the Central Universities (No. JBK 1805006).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China (NSFC).