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Asymptotic stability of a Bloch skyrmion for the Landau-Lifshitz-Gilbert equation

  • Jordan Berthoumieu
  • Raphaël Côte
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Abstract

We prove the asymptotic stability of isolated skyrmions under the flow of the two-dimensional Landau-Lifshitz-Gilbert equation. We consider a micromagnetic energy functional involving the exchange energy, the Dzyaloshinskii-Moriya interaction, and the Zeeman interaction. We are interested in the stability of chiral Bloch skyrmions, which are local minimizers of this energy. We prove that data in H2 which are near in the skyrmion in a slighlty stronger than H1 sense, converge with exponential rate, in H2, to the skyrmion, up to a change of gauge.

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Cite

BibTeXRIS
BibTeX
@misc{berthoumieu2026asymptotic,
  title = {{Asymptotic stability of a Bloch skyrmion for the Landau-Lifshitz-Gilbert equation}},
  author = {Jordan Berthoumieu and Raphaël Côte},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23753},
  eprint = {2610.23753},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05804938v1},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Asymptotic stability of a Bloch skyrmion for the Landau-Lifshitz-Gilbert equation
AU  - Jordan Berthoumieu
AU  - Raphaël Côte
PY  - 2026
DA  - 2026/10/16
PB  - HAL
DO  - 10.48550/arxiv.2610.23753
UR  - https://hal.science/hal-05804938v1
AB  - We prove the asymptotic stability of isolated skyrmions under the flow of the two-dimensional Landau-Lifshitz-Gilbert equation. We consider a micromagnetic energy functional involving the exchange energy, the Dzyaloshinskii-Moriya interaction, and the Zeeman interaction. We are interested in the stability of chiral Bloch skyrmions, which are local minimizers of this energy. We prove that data in H2 which are near in the skyrmion in a slighlty stronger than H1 sense, converge with exponential rate, in H2, to the skyrmion, up to a change of gauge.
ER  -