Limiting vorticities for the Ginzburg-Landau equations. (Q1413727)

The asymptotic limit of solutions to the Ginzburg-Landau equations in two dimensions is investigated. The authors study the Ginzburg-Landau system with magnetic field describing a superconductor in an applied magnetic field in the ``London limit'' of a Ginzburg-Landau parameter \(\kappa\) tending to infinity. The asymptotic behavior is examined of the ``vorticity measures'' associated to the vortices of the solution and it is proved that passing to the limit in the equation (via the ``stress-energy tensor'') yields a criticality condition on the limiting measures. That condition allows to describe the possible locations and densities of the vortices. Analogous results are established for the Ginzburg-Landau equation without magnetic field as well.