IUMJ

Title: Stability in $2D$ Ginzburg-Landau passes to the limit

Authors: Sylvia Serfaty

Issue: Volume 54 (2005), Issue 1, 199-222

Abstract:

We prove that if we consider a family of \textit{stable} solutions to the Ginzburg-Landau equation, then their vortices converge to a \textit{stable} critical point of the ``renormalized energy.'' Moreover, in the case of instability, the number of ``directions of descent'' is bounded below by the number of directions of descent for the renormalized energy. A consequence is a result of nonexistence of stable nonconstant solutions to Ginzburg-Landau with homogeneous Neumann boundary condition.