Spinor Ginzburg–Landau equation and mean curvature flow Original Research Article

Recent papers in the physics literature have introduced spin-coupled (or spinor) Ginzburg–Landau models for complex vector-valued order parameters in order to account for ferromagnetic or antiferromagnetic effects in high-temperature superconductors. In this paper, we study the asymptotic behavior of solutions of the evolutionary spinor Ginzburg–Landau equation in three dimensions. We prove also that, asymptotically, the singularities evolve according to mean curvature flow in the sense of weak formulation.