Dynamics of the GinzburgLandau equations of superconductivity, Nonlinear Analysis

Abstract. This article is concerned with the Ginzburg{Landau (GL) equations of superconductivity. The equations provide a mathematical model for the study of magnetic ux vortices in superconductors. The focus is on the asymptotic case when the charge of the superconducting charge carriers (Cooper pairs) is vanishingly small and the applied magnetic eld approaches the upper critical eld. It is shown that the GL model reduces in the limit to the frozen-eld model, where the superconduct-ing phenomena are aected by the electromagnetic phenomena, but not vice versa. The convergence is second order in the small parameter. The analytical results are con rmed in some numerical examples.