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

@article{Fan2012UniquenessOW,
  title={Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity},
  author={Jishan Fan and Tohru Ozawa},
  journal={Zeitschrift f{\"u}r angewandte Mathematik und Physik},
  year={2012},
  volume={63},
  pages={453-459}
}
We prove the uniqueness for weak solutions of the time-dependent 2-D Ginzburg-Landau model for superconductivity with L2 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 L2 initial data. 
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