Inserted: 28 feb 2009
Last Updated: 10 aug 2009
Journal: Boll. Unione Mat. Ital. (9)
We consider an energy functional on measures in $R^2$ arising in superconductivity as a limit case of the well-known Ginzburg Landau functionals. We study its gradient flow with respect to the Wasserstein metric of probability measures, whose corresponding time evolutive problem can be seen as a mean field model for the evolution of vortex densities. We obtain a new existence and uniqueness result for this problem.