Abstract and Applied Analysis 
Volume 2005 (2005), Issue 8, Pages 863-887
doi:10.1155/AAA.2005.863

Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity

Fouzi Zaouch

 Laboratoire de Mathématiques et Applications (L.M.A.), Pôle Sciences et Technologies, Université de La Rochelle, Avenue Michel Crépeau, La Rochelle Cedex 17042, France
Received 15 April 2004

Abstract

The time-dependent Ginzburg-Landau equations of superconductivity with a time-dependent magnetic field H are discussed. We prove existence and uniqueness of weak and strong solutions with H1-initial data. The result is obtained under the “φ=−ω(∇⋅A)” gauge with ω>0. These solutions generate a dynamical process and are uniformly bounded in time.