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Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation

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Abstract

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg–Landau vortices for sphere-valued maps. In particular, we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization are ruled by the Landau–Lifshitz–Gilbert equation, which combines characteristic properties of a nonlinear Schrödinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation.

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Authors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Matthias Kurzke

  2. Department of Mathematics I, RWTH Aachen University, 52056, Aachen, Germany

    Christof Melcher

  3. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK

    Roger Moser

  4. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Daniel Spirn

Authors
  1. Matthias Kurzke
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  2. Christof Melcher
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  3. Roger Moser
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  4. Daniel Spirn
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Corresponding author

Correspondence to Roger Moser.

Additional information

Communicated by A. Mielke

Part of this research was carried out while the authors enjoyed the hospitality of the Hausdorff Research Institute for Mathematics in Bonn. Matthias Kurzke was partially supported by DFG SFB 611; Daniel Spirn was partially supported by NSF grant DMS-0707714.

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Kurzke, M., Melcher, C., Moser, R. et al. Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation. Arch Rational Mech Anal 199, 843–888 (2011). https://doi.org/10.1007/s00205-010-0356-0

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  • DOI: https://doi.org/10.1007/s00205-010-0356-0

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