Vortices in a Stochastic Parabolic Ginzburg-Landau Equation

Abstract

We consider the variant of a stochastic parabolic Ginzburg-Landau equation that allows for the formation of point defects of the solution. The noise in the equation is multiplicative of the gradient type. We show that the family of the Jacobians associated to the solution is tight on a suitable space of measures. Our main result is the characterization of the limit points of this family. They are concentrated on finite sums of delta measures with integer weights. The singular set of the solution coincides with the points at which the delta measures are centered.

Final version; to appear in "Stochastics and Partial Differential Equations: Analysis and Computations"