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

Article

DOI: 10.1007/s00033-011-0164-x

Cite this article as:
Fan, J. & Ozawa, T. Z. Angew. Math. Phys. (2012) 63: 453. doi:10.1007/s00033-011-0164-x

Abstract

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.

Mathematics Subject Classification (2000)

35K55 

Keywords

Uniqueness Ginzburg-Landau model Superconductivity Coulomb gauge Lorentz gauge 

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsNanjing Forestry UniversityNanjingPeople’s Republic of China
  2. 2.Department of Applied PhysicsWaseda UniversityTokyoJapan

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