WELL POSEDNESS FOR A PHASE TRANSITION MODEL IN SUPERCONDUCTIVITY WITH VELOCITY AND MAGNETIC CRITICAL FIELDS

Abstract

In this paper we present a Ginzburg–Landau model to describe the phenomenon of superconductivity as a second-order phase transition. The model proposed, which also includes thermal effects, allows to explain the existence of threshold values, both of the magnetic field and of the superconducting current, beyond which superconductivity vanishes. This is achieved by introducing a constitutive equation for the magnetic induction where the magnetic permeability depends on the complex order parameter. The model is proved to be consistent with thermodynamical principles. The resulting differential system is studied under the assumption that the temperature is a fixed parameter and its well-posedness is proved.