Global well-posedness of axially symmetric weak solutions to the Ginzburg–Landau model in superconductivity

ABSTRACT

This paper proves global existence and uniqueness of axially symmetric weak solutions to the 3D time-dependent Ginzburg–Landau model in superconductivity in ${\mathbb{R}}^3$ with $L^2$ initial data and the choice of Lorentz gauge. We are unable to prove a similar result with the Coulomb gauge.

COMMUNICATED BY:

• B. R. Vainberg

KEYWORDS:

• Uniqueness
• weak solutions
• superconductivity

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 35K55

Acknowledgments

The authors are indebted to the referee for adding the ‘Remark 1.2’.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Miaochao Chen http://orcid.org/0000-0002-6003-9033

Additional information

Funding

This paper is supported by the project of Natural Science Research of Chaohu University in 2015 (XLY-201503); the key project of University Natural Science of Anhui Province (nos. KJ2017A453, KJ2017A454).