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VORTEX LIQUIDS AND THE GINZBURG–LANDAU EQUATION

Part of: Parabolic equations and systems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  27 May 2014

MATTHIAS KURZKE  and
DANIEL SPIRN
MATTHIAS KURZKE
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK; matthias.kurzke@nottingham.ac.uk
DANIEL SPIRN
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA; spirn@math.umn.edu

Abstract

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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.

MSC classification

Secondary: 35Q56: Ginzburg-Landau equations 35K51: Initial-boundary value problems for second-order parabolic systems
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 2 , 01 July 2014 , e11
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
© The Author(s) 2014

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