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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China

    Jishan Fan

  2. Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan

    Tohru Ozawa

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  1. Jishan Fan
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  2. Tohru Ozawa
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Correspondence to Tohru Ozawa.

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Supported by NSFC (Grant No. 10301014).

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Fan, J., Ozawa, T. Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity. Z. Angew. Math. Phys. 63, 453–459 (2012). https://doi.org/10.1007/s00033-011-0164-x

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  • DOI: https://doi.org/10.1007/s00033-011-0164-x

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