Electron. J. Differential Equations, Vol. 2020 (2020), No. 17, pp. 1-6.

Existence and uniqueness for a Ginzburg-Landau system for superconductivity

Jishan Fan, Yong Zhou

We prove the existence of a unique solution for a time-dependent Ginzburg-Landau model in superconductivity under the Coulomb gauge. Also we prove the uniform-in- $\epsilon$ well-posedness of the solution, where $\epsilon$ is the coefficient of the double-well potential energy.

Submitted December 6, 2019. Published February 11, 2020.
Math Subject Classifications: 35Q35, 35K55.
Key Words: Ginzburg-Landau model; superconductivity; Coulomb gauge.

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Jishan Fan
Department of Applied Mathematics
Nanjing Forestry University
Nanjing 210037, China
email: fanjishan@njfu.edu.cn
  Yong Zhou
School of Mathematics (Zhuhai)
Sun Yat-sen University
Zhuhai, Guangdong 519082, China
email: zhouyong3@mail.sysu.edu.cn

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