Global existence and uniqueness of solutions of the time-dependent ginzburg-landau model for superconductivity

Abstract

We consider the initial-boundary value problems of the timc-dependmt nodnear Ginzburg-Landau equations in superconductivity. It is assumed that the material sample occupies a bounded domain in two nd three dimensional spaces. LVe illustrate that the original equations are not well-posed. In order to fix the lack of niqueness of the solutions, possible choices of the gauge are identified. Global existence and uniqueness of solutions re proved in a proper gauge. A by-product is the convergence of finite-dimensional Galerkin approximations whichmay be used in the numerical study of superconductivity phenomena.