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On the vortex filament conjecture for the Gross-Pitaevskii equation

  • Manuel del Pino
  • Rowan Juneman
  • Monica Musso
  • Juncheng Wei
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Abstract

We establish one form of the vortex filament conjecture for the three-dimensional Gross-Pitaevskii equation. Given any smooth closed embedded binormal flow of curves on a compact time interval, we construct, in the small-core limit ε→0, a family of exact solutions whose degree-one vortex filaments converge uniformly to the prescribed flow. Near the filament the solutions have the standard planar vortex profile, while away from it their phase gradients converge to the associated Biot-Savart field. We also derive a refined modulation law for the vortex filament.

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Cite

BibTeXRIS
BibTeX
@misc{pino2026vortex,
  title = {{On the vortex filament conjecture for the Gross-Pitaevskii equation}},
  author = {Manuel del Pino and Rowan Juneman and Monica Musso and Juncheng Wei},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13078},
  eprint = {2609.13078},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13078},
}
RIS
TY  - UNPB
TI  - On the vortex filament conjecture for the Gross-Pitaevskii equation
AU  - Manuel del Pino
AU  - Rowan Juneman
AU  - Monica Musso
AU  - Juncheng Wei
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.13078
UR  - https://arxiv.org/abs/2609.13078
AB  - We establish one form of the vortex filament conjecture for the three-dimensional Gross-Pitaevskii equation. Given any smooth closed embedded binormal flow of curves on a compact time interval, we construct, in the small-core limit ε→0, a family of exact solutions whose degree-one vortex filaments converge uniformly to the prescribed flow. Near the filament the solutions have the standard planar vortex profile, while away from it their phase gradients converge to the associated Biot-Savart field. We also derive a refined modulation law for the vortex filament.
ER  -