Refined Jacobian estimates and the Gross-Pitaevsky equations

The Gross-Pitaevsky equations serve as an excellent model for superfluids. One important feature of superfluids is the formation of very tight vortices that rotate with the liquid helium. In the theoretical model, a very tight vortex corresponds to a very large Ginzburg-Landau constant. In the limit of large Ginzburg-Landau constant, it has been previously shown that these vortices move according to the same classical ODE as point vortices do in two-dimensional incompressible, inviscid fluids. I will present joint work with R. Jerrard concerning the proof of this motion law for large, but fixed, Ginzburg-Landau constant. The primary tools will be sharp and near sharp estimates of the Jacobian.