Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity

Jishan Fan; Tohru Ozawa

doi:10.1007/s00033-011-0164-x

Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity

Jishan Fan, Tohru Ozawa^*

^*Corresponding author for this work

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

We prove the uniqueness for weak solutions of the time-dependent 2-D Ginzburg-Landau model for superconductivity with L ² initial data in the case of Coulomb gauge. This question was left open in Tang and Wang (Physica D, 88:139-166, 1995). We also prove the uniqueness of the 3-D radially symmetric solution in bounded annular domain with the choice of Lorentz gauge and L ² initial data.

Original language	English
Pages (from-to)	453-459
Number of pages	7
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	63
Issue number	3
DOIs	https://doi.org/10.1007/s00033-011-0164-x
Publication status	Published - 2012 Jun

Keywords

Coulomb gauge
Ginzburg-Landau model
Lorentz gauge
Superconductivity
Uniqueness

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

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10.1007/s00033-011-0164-x

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abstract = "We prove the uniqueness for weak solutions of the time-dependent 2-D Ginzburg-Landau model for superconductivity with L 2 initial data in the case of Coulomb gauge. This question was left open in Tang and Wang (Physica D, 88:139-166, 1995). We also prove the uniqueness of the 3-D radially symmetric solution in bounded annular domain with the choice of Lorentz gauge and L 2 initial data.",

keywords = "Coulomb gauge, Ginzburg-Landau model, Lorentz gauge, Superconductivity, Uniqueness",

author = "Jishan Fan and Tohru Ozawa",

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AU - Ozawa, Tohru

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N2 - We prove the uniqueness for weak solutions of the time-dependent 2-D Ginzburg-Landau model for superconductivity with L 2 initial data in the case of Coulomb gauge. This question was left open in Tang and Wang (Physica D, 88:139-166, 1995). We also prove the uniqueness of the 3-D radially symmetric solution in bounded annular domain with the choice of Lorentz gauge and L 2 initial data.

AB - We prove the uniqueness for weak solutions of the time-dependent 2-D Ginzburg-Landau model for superconductivity with L 2 initial data in the case of Coulomb gauge. This question was left open in Tang and Wang (Physica D, 88:139-166, 1995). We also prove the uniqueness of the 3-D radially symmetric solution in bounded annular domain with the choice of Lorentz gauge and L 2 initial data.

KW - Coulomb gauge

KW - Ginzburg-Landau model

KW - Lorentz gauge

KW - Superconductivity

KW - Uniqueness

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Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity

Abstract

Keywords

ASJC Scopus subject areas

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