Pith Number

pith:ETMOLWQK

pith:2026:ETMOLWQKLRAN5HOV657KM5OFRY

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The Energy Based Near Singularity for Fourier Spectral 3D Navier-Stokes Equations

Beibei Li

Fourier spectral discretization of the 3D Navier-Stokes equations converges exponentially in space while an energy-based criterion links numerical blowup to loss of regularity.

arxiv:2604.23159 v2 · 2026-04-25 · math.NA · cs.NA

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4 Citations 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

We prove exponential convergence in space, algebraic convergence in time, and an a posteriori criterion that links numerical blowup to loss of regularity.

C2weakest assumption

The resolution conditions and spectral accuracy assumptions hold uniformly for the chosen Fourier basis and time-stepping scheme when the solution remains in the regularity class under study.

C3one line summary

An energy-based conditional regularity framework and a posteriori diagnostics are derived for Fourier spectral discretizations of the 3D Navier-Stokes equations to detect potential finite-time singular behavior.

Receipt and verification

First computed	2026-05-20T00:02:11.798660Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24d8e5da0a5c40de9dd5f77ea675c58e354dceb72a2a6ff5719daa477cb2ec3e

Aliases

arxiv: 2604.23159 · arxiv_version: 2604.23159v2 · doi: 10.48550/arxiv.2604.23159 · pith_short_12: ETMOLWQKLRAN · pith_short_16: ETMOLWQKLRAN5HOV · pith_short_8: ETMOLWQK

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ETMOLWQKLRAN5HOV657KM5OFRY \
  | 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: 24d8e5da0a5c40de9dd5f77ea675c58e354dceb72a2a6ff5719daa477cb2ec3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ac8679ed9067c5e5989b7d39f6b8f22e0032db8c60d485cef0c325b4c84f322",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-04-25T06:12:04Z",
    "title_canon_sha256": "1653eed1ece67eb5a7b36fb169f75af2885fec55db2e95faf3ef38d2e8bad0b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.23159",
    "kind": "arxiv",
    "version": 2
  }
}