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.
"Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity." Abstr. Appl. Anal. 2005 (8) 863 - 887, 16 October 2005. https://doi.org/10.1155/AAA.2005.863