VORTEX LIQUIDS AND THE GINZBURG–LANDAU EQUATION

Abstract 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.

• Publication year

  2011

• Venue

  Forum of Mathematics, Sigma

• Publication date

  2011-05-24

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1017/fms.2014.6arXiv 1105.4781
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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