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. Since different choices of gauge lead to a different representation of such variables, the classical formulations of the Ginzburg Landau model do not allow to establish the property of gauge-invariance. With a suitable decomposition of the unknown fields, we write the problem in terms of real variables and deduce some energy estimates which prove the existence of a maximal attractor for the system.