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

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.