A non-existence result for the Ginzburg-Landau equations

TL;DR

This paper demonstrates that for certain applied magnetic fields, including constant fields, the stationary Ginzburg-Landau equations in two and three dimensions do not have finite energy solutions, revealing fundamental limitations.

Contribution

It establishes a non-existence result for finite energy solutions of the Ginzburg-Landau equations under specific magnetic field conditions.

Findings

Certain magnetic fields prevent finite energy solutions

Constant magnetic fields are among the non-existence cases

Results apply to both 2D and 3D settings

Abstract

We consider the stationary Ginzburg-Landau equations in $\R^d$, $d=2,3$. We exhibit a class of applied magnetic fields (including constant fields) such that the Ginzburg-Landau equations do not admit finite energy solutions.