On the hydrodynamic limit of Ginzburg-Landau vortices

Introduction.This is a continuation of our early studies L], LX] on the dynamics of the Ginzburg-Landau vortices, see also JS].Here we are interested in issues related to the hydrodynamic limit of the nite vortices dynamics studied in L] and LX].Our main motivation for studying these issues comes from the type-II superconductivity.In the classical mean-eld picture, the phase diagram in the H ;T plane (see Ti]) consists of three parts.In the Meisser phase T < T c H < H c1 (T )], magnetic ux does not penetrate into the material sample.In the mixed phase T < T c H c1 (T ) < H < H c2 (T )], magnetic ux penetrates the sample as quantized vortices and forms the well-known Abrikosov lattice.The remaining part of the ZZ] Zhang, P. Zheng, Y. On the Existence and Uniqueness of Solutions to an Asymptotic Equation of a Variational Wave Equation, Academia Mathematica, (in press).