Asymptotic behaviour of time-dependent Ginzburg-Landau equations of superconductivity

Abstract

In this paper, we establish the global fast dynamics for the time-dependent Ginzburg-Landau equations of superconductivity. We show the squeezing property and the existence of finite-dimensional exponential attractors for the system. In addition we prove the existence of the global attractor in L-2 x L-2 for the Ginzburg-Landau equations in two spatial dimensions.