Uniform existence and uniqueness for a time-dependent Ginzburg-Landau model for superconductivity

Abstract

We study the initial boundary value problem for a time-dependent Ginzburg-Landau model of superconductivity. First, we prove the uniform boundedness of strong solutions with respect to diffusion parameter > 0 in the case of Coulomb gauge for 2D case. Our second result is the uniqueness of axially symmetric weak solutions in 3D with L2 initial data under Lorentz gauge. Mathematics Subject Classifications: 35K55