Pith Number

pith:7XDUWDII

pith:2026:7XDUWDII3US4FOPCTMBMEIUDUG

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Finite-time blow-up in an elementary model of the 3D Navier-Stokes equations

Stan Palasek

A realistic shell model of the 3D Navier-Stokes equations develops finite-time blow-up from smooth initial data and forcing.

arxiv:2605.13827 v1 · 2026-05-13 · math.AP

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4 Citations open

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Claims

C1strongest claim

We demonstrate finite-time blow-up in a simple, realistic shell model of the 3D Navier-Stokes equations, equipped with smooth (rapidly decaying in frequency) initial data and forcing.

C2weakest assumption

The chosen shell interactions are sufficiently faithful to the true Euler nonlinearity that the observed blow-up is not an artifact of the reduction; the paper itself notes that prior models used highly artificial interactions.

C3one line summary

A dyadic shell model of the 3D Navier-Stokes equations exhibits finite-time blow-up from smooth initial data and forcing, with singularity formation also shown in the inviscid unforced case just above the energy level.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] D. Barbato, F. Morandin, and M. Romito. Smooth solutions for the dyadic model.Nonlinearity, 24(11):3083–3097, 2011 2011

[2] A. Cheskidov. Blow-up in finite time for the dyadic model of the Navier-Stokes equations.Trans. Amer. Math. Soc., 360(10):5101–5120, 2008 2008

[3] A. Cheskidov, M. Dai, and S. Friedlander. Dyadic models for fluid equations: a survey.J. Math. Fluid Mech., 25(3):Paper No. 62, 26, 2023 2023

[4] [CKS97] Russel E 2025

[5] A. Cheskidov, S. Friedlander, and N. Pavlovi´ c. Inviscid dyadic model of turbulence: the fixed point and Onsager’s conjecture.J. Math. Phys., 48(6):065503, 16, 2007 2007

Receipt and verification

First computed	2026-05-18T02:44:15.140642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdc74b0d08dd25c2b9e29b02c22283a1bfb3665049c3e45e79fb3e3a6badf063

Aliases

arxiv: 2605.13827 · arxiv_version: 2605.13827v1 · doi: 10.48550/arxiv.2605.13827 · pith_short_12: 7XDUWDII3US4 · pith_short_16: 7XDUWDII3US4FOPC · pith_short_8: 7XDUWDII

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7XDUWDII3US4FOPCTMBMEIUDUG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fdc74b0d08dd25c2b9e29b02c22283a1bfb3665049c3e45e79fb3e3a6badf063

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c46245522c6d449f92e6087afdedaf6bab2ab79428cb8db24fcc575d03628faf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T17:51:21Z",
    "title_canon_sha256": "535827ae856353ad8ac20302d752c4ba0d7ca225ed873b733b094bdcb045a040"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13827",
    "kind": "arxiv",
    "version": 1
  }
}