Stability in 2D Ginzburg-Landau passes to the limit
Stéphane Serfaty · Indiana University Mathematics Journal · 2005
We prove that if we consider a family of stable solutions to the Ginzburg-Landau equation, then their vortices converge to a 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.