Pith Number

pith:MIOC4DOM

pith:2024:MIOC4DOMZ2N4DZGAO24WUBA57X

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Non-Smooth Solutions of the Navier-Stokes Equation

J. Glimm, J. Petrillo

Non-smooth Leray-Hopf solutions to the Navier-Stokes equations are constructed and blow up in finite time.

arxiv:2410.09261 v8 · 2024-10-11 · math.AP · hep-th · math-ph · math.MP

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\pithnumber{MIOC4DOMZ2N4DZGAO24WUBA57X}

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Record completeness

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Non-smooth Leray-Hopf solutions of the Navier-Stokes equation are constructed. The proof of finite time blowup is based on analyticity properties of the weak solutions of the Navier-Stokes equation. The turbulent initial data is characterized in terms of its expansion in spherical harmonics basis functions.

C2weakest assumption

The selection of entropy production maximizing solutions with turbulent initial data, characterized via spherical harmonics expansion, produces non-smooth behavior whose finite-time blowup follows from analyticity properties of weak solutions (abstract, no further specification of the analyticity argument or the entropy functional).

C3one line summary

Constructs non-smooth Leray-Hopf weak solutions to 3D Navier-Stokes in periodic cube T3 with finite-time blowup, using entropy-maximizing turbulent initial data expanded in spherical harmonics; mean value is smooth.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-27T01:04:47.373962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

621c2e0dccce9bc1e4c076b96a041dfde42b5ba3099973748987a3350d5eacb1

Aliases

arxiv: 2410.09261 · arxiv_version: 2410.09261v8 · doi: 10.48550/arxiv.2410.09261 · pith_short_12: MIOC4DOMZ2N4 · pith_short_16: MIOC4DOMZ2N4DZGA · pith_short_8: MIOC4DOM

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MIOC4DOMZ2N4DZGAO24WUBA57X \
  | 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: 621c2e0dccce9bc1e4c076b96a041dfde42b5ba3099973748987a3350d5eacb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b4c110295dddd11606f61b2d5674b344625c1523433120b1fd53cf45f57d5bd",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-10-11T21:25:05Z",
    "title_canon_sha256": "99c577c991ee7d7712006fb9cd26ad113d78f8052cdc8cd384668189afacd374"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.09261",
    "kind": "arxiv",
    "version": 8
  }
}