Pith Number

pith:HRA4DP66

pith:2026:HRA4DP66SMBAVEODW7SLZT3D37

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Exact conservation and the Onsager threshold: a discrete exterior calculus theory for incompressible Navier--Stokes

Peter Korn

Exact algebraic conservation in a discrete scheme rules out dissipative weak solutions of the Euler equations.

arxiv:2605.13048 v1 · 2026-05-13 · math.AP · cs.NA · math.NA

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Claims

C1strongest claim

exact algebraic conservation at the discrete level is not merely a fidelity property but rules out entire classes of weak solutions that other discretisations reach unconditionally

C2weakest assumption

the discrete solutions admit a uniform C^{0,α} bound there (for the inviscid measure-valued regime above the Onsager threshold)

C3one line summary

A structure-preserving DEC discretization of incompressible fluids enforces exact conservation, ruling out dissipative Euler weak solutions and ensuring conservative measure-valued solutions above the Onsager threshold under regularity bounds.

References

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[1] Finiteelementexteriorcalculus, homological techniques, and applications.Acta Numer., 15:1–155, 2006 2006

[2] D. N. Arnold, R. S. Falk, and R. Winther. Finite element exterior calculus: from Hodge theory to numerical stability.Bull. Amer. Math. Soc. (N.S.), 47(2):281–354, 2010. 72 2010

[3] V. I. Arnold. Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits.Annales de l’Institut Fourier, 16(1):319–361, 1966 1966

[4] L. C. Berselli, T. Iliescu, and W. J. Layton.Mathematics of Large Eddy Simulation of Turbulent Flows. Scientific Computation. Springer, Berlin, 2006 2006

[5] A. Bossavit. Whitney forms: a class of finite elements for three-dimensional compu- tations in electromagnetism.IEE Proc. A, 135(8):493–500, 1988 1988

Receipt and verification

First computed	2026-05-18T03:08:59.382002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c41c1bfde93020a91c3b7e4bccf63dfd7da0e71d283e496f3075dda779711dc

Aliases

arxiv: 2605.13048 · arxiv_version: 2605.13048v1 · doi: 10.48550/arxiv.2605.13048 · pith_short_12: HRA4DP66SMBA · pith_short_16: HRA4DP66SMBAVEOD · pith_short_8: HRA4DP66

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HRA4DP66SMBAVEODW7SLZT3D37 \
  | 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: 3c41c1bfde93020a91c3b7e4bccf63dfd7da0e71d283e496f3075dda779711dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6190c1e9eba8864dd689ec1087fc49f730047a6981e5c8965e70cd2d5909c62",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T06:12:26Z",
    "title_canon_sha256": "bfd0767e3136913cd0ca7747c58b0aa8769148b4b766fd4c70eb407cdc05af79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13048",
    "kind": "arxiv",
    "version": 1
  }
}