Uniform existence for a 3D time-dependent Ginzburg-Landau model in superconductivity

In this paper, we prove the uniform-in-κ existence for the 3D time-dependent Ginzburg-Landau model (TDGL) in superconductivity in the case of the Coulomb gauge, where κ is the Ginzburg-Landau constant. Consequently, the limit as κ→0 can be established.