Weak solutions to the Ginzburg-Landau model in superconductivity with the Coulomb gauge

We first prove the uniqueness of weak solutions (ψ,A) to the 3-D Ginzburg–Landau model in superconductivity with zero magnetic diffusivity and the Coulomb gauge if (ψ,A)∈W:=(ψ,A)ψ∈L20,T;L∞∩L20,T;H1,A∈C[0,T];L3, which is a critical space for some positive constant T. We also prove the global existence of solutions when ψ0∈L∞∩W23,32 and A0∈L3. Copyright © 2016 John Wiley & Sons, Ltd.