A reduced Ginzburg–Landau model in ℝⁿ

ABSTRACT

In this work, we consider a reduced Ginzburg–Landau model in which the magnetic field is neglected. First, we show the well-posedness of weak solutions and strong solutions in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$. Finally, we prove the well-posedness of smooth solutions when $\mathrm{\Omega }:={\mathbb{R}}^n(n\ge 3)$.

Keywords:

• Ginzburg–Landau
• superconductivity
• uniqueness

Mathematics Subject Classifications (2010):

• 82D55
• 35Q56

Acknowledgments

We are very much indebted to the referee for a very careful reading of the manuscript and for many helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

J. Fan is partially supported by NSFC (No. 11971234). Tong Tang is partially supported by NSFC (No. 11801138).