Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents

Abstract

In this work we consider a reduced Ginzburg-Landau model in which the magnetic field is neglected and the magnitude of the current density is significantly stronger than that considered in a recent work by the same authors. We prove the existence of a solution which can be obtained by solving a non-convex minimization problem away from the boundary of the domain. Near the boundary, we show that this solution is essentially one-dimensional. We also establish some linear stability results for a simplified, one-dimensional version of the original problem.

References in corpus (3)

• Bifurcation diagram and pattern formation in superconducting wires with electric currents
• Global stability of the normal state of superconductors in the presence of a strong electric current
• Qualitative modifications and new dynamic phases in the phase diagram of 1D superconducting wires driven with electric currents