Gauge invariance and asymptotic behavior for the Ginzburg-Landau equations of superconductivity

In this paper we study the gauge invariance of the time-dependent Ginzburg-Landau equations through the introduction of a model which uses observable variables. We observe that the various choices of gauge lead to a different representation of such variables and therefore to a different definition of the weak solution of the problem. With a suitable decomposition of the unknown fields, related to the choice of London gauge, we examine the Ginzburg-Landau equations and deduce some energy estimates which prove the existence of a maximal attractor for the system.