On the Ginzburg–Landau model of a superconducting ball in a uniform field

We consider the three-dimensional Ginzburg–Landau model for a solid spherical superconductor in a uniform magnetic field, in the limit as the Ginzburg–Landau parameter \kappa = 1/ ɛ\rightarrow \infty . By studying a limiting functional, we identify a candidate for the lower critical field H_{c_{1}} , the value of the applied field strength at which minimizers first exhibit vortices. For applied fields of this strength we show the existence …