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PreprintCC BY 4.0arXiv

An eps-regularity criterion at one scale for 3-D Navier-Stokes equations and improved upper bound on the box dimension of the interior singular set

  • Yi Lu
  • Rongrong Chi
  • Wei Ren
Open at sourcePDFDOICite

Abstract

In this paper, we obtain an ε-regularity criterion at one scale for 3D Navier-Stokes equations using a coarse-to-refined estimate argument based on mean-fluctuation decomposition. Making use of this ε-regularity criterion, we improve the upper bound on the box dimension of the interior singular set to 15/13.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026epsregularity,
  title = {{An $\eps$-regularity criterion at one scale for 3-D Navier-Stokes equations and improved upper bound on the box dimension of the interior singular set}},
  author = {Yi Lu and Rongrong Chi and Wei Ren},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17569},
  eprint = {2610.17569},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17569},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An eps-regularity criterion at one scale for 3-D Navier-Stokes equations and improved upper bound on the box dimension of the interior singular set
AU  - Yi Lu
AU  - Rongrong Chi
AU  - Wei Ren
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17569
UR  - https://arxiv.org/abs/2610.17569
AB  - In this paper, we obtain an ε-regularity criterion at one scale for 3D Navier-Stokes equations using a coarse-to-refined estimate argument based on mean-fluctuation decomposition. Making use of this ε-regularity criterion, we improve the upper bound on the box dimension of the interior singular set to 15/13.
ER  -