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PreprintCC BY 4.0arXiv

Global well-posedness of the 3D Navier-Stokes equations with helical L1 vorticity

  • Francisco Gancedo
  • Antonio Hidalgo-Torné
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Abstract

We show that the Navier-Stokes equations on ℝ2×𝕋 are globally well posed for initial vorticities that are both helically symmetric and integrable. This class of data typically generates velocity fields of infinite kinetic energy, so this result is not covered by the classical finite-energy well-posedness theory. This result is supercritical from the perspective of the three-dimensional Navier-Stokes scaling, and it is made possible by the special structure of helical flows using time-weighted Kato-type spaces.

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Cite

BibTeXRIS
BibTeX
@misc{gancedo2026global,
  title = {{Global well-posedness of the 3D Navier-Stokes equations with helical $L^1$ vorticity}},
  author = {Francisco Gancedo and Antonio Hidalgo-Torné},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05193},
  eprint = {2609.05193},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05193},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Global well-posedness of the 3D Navier-Stokes equations with helical L^1 vorticity
AU  - Francisco Gancedo
AU  - Antonio Hidalgo-Torné
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05193
UR  - https://arxiv.org/abs/2609.05193
AB  - We show that the Navier-Stokes equations on ℝ^2×𝕋 are globally well posed for initial vorticities that are both helically symmetric and integrable. This class of data typically generates velocity fields of infinite kinetic energy, so this result is not covered by the classical finite-energy well-posedness theory. This result is supercritical from the perspective of the three-dimensional Navier-Stokes scaling, and it is made possible by the special structure of helical flows using time-weighted Kato-type spaces.
ER  -