Abstract and Applied Analysis
Volume 2005 (2005), Issue 8, Pages 863-887
Existence and uniform boundedness of strong solutions of
the time-dependent Ginzburg-Landau equations of superconductivity
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
Copyright © 2005 Fouzi Zaouch. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The time-dependent Ginzburg-Landau equations of superconductivity
with a time-dependent magnetic field are discussed. We prove existence and uniqueness of weak and strong
solutions with -initial data. The result is obtained under
the “” gauge with .
These solutions generate a dynamical process and are uniformly
bounded in time.