The long-time behavior of the transient Ginzburg-Landau model for superconductivity II Original Research Article

In this paper we prove that the global existence, uniqueness of the solution of a Ginzburg-Landau superconductivity model with the assumptions that the initial data (View the MathML source only. Under suitable choice of gauge, say, the Lorentz gauge or the Coulomb gauge, we prove that the solutions of the evolutionary superconductivity model must subconverge strongly in H2(Ω) × H2(Ω) to one of the solutions of the stationary problem in the Coulomb gauge as time goes to infinity. Because we know little about the number of solutions of the corresponding stationary problem, we can only prove subconvergence in time. However, we can also prove the existence of a maximal attractor in L2(Ω) × L2(Ω) and of an inertial set under the Lorentz gauge.