Vortex liquids and the Ginzburg-Landau equation

Details Vortex liquids and the Ginzburg-Landau equation Vortex liquids and the Ginzburg-Landau equation

2011-05-24

arxiv.org/abs/1105.4781v1

Mathematics

Analysis of PDEs

Scientific paper

We establish vortex dynamics for the time-dependent Ginzburg-Landau equation for asymptotically large numbers of vortices for the problem without a gauge field and either Dirichlet or Neumann boundary conditions. As our main tool, we establish quantitative bounds on several fundamental quantities, including the kinetic energy, that lead to explicit convergence rates. For dilute vortex liquids we prove that sequences of solutions converge to the hydrodynamic limit.

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