On stability of Abrikosov vortex lattices

We study stability of Abrikosov vortex lattices under finite energy perturbations satisfying a natural parity condition (both defined precisely in the text) for the dynamics given by the Gorkov-Eliashberg-Schmid equations. For magnetic fields close to the second critical magnetic field and for arbitrary lattice shapes, we prove that there exist two functions on the space of lattices, such that Abrikosov vortex lattice solutions are asymptotically stable, provided the superconductor is of Type II and these functions are positive, and unstable, for superconductors of Type I, or if one of these functions is negative.