Pith Number

pith:RWZI4U3O

pith:2026:RWZI4U3O66XNVFVBJE4UHKNGXW

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Liouville Theorems Above the Critical $9/2$ Threshold for Stationary Navier-Stokes Equations

Gaston Vergara-Hermosilla

Stationary Navier-Stokes flows in three dimensions are necessarily zero when their velocity is integrable to an order strictly above 9/2.

arxiv:2604.06527 v2 · 2026-04-07 · math.AP

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Claims

C1strongest claim

We prove that triviality already follows under assumptions of the form u ∈ L^{9/2 + ε(·)}(R^3), where ε(·)>0. As a consequence, we obtain a localized Liouville theorem: it is sufficient to impose this integrability condition only at infinity, with no additional assumptions on the behavior of u inside a compact set.

C2weakest assumption

The velocity u belongs to a weak solution class for the stationary Navier-Stokes system, and the variable exponent ε(·) satisfies the technical conditions needed for the Lebesgue space with variable exponents to support the general uniqueness result invoked in the proof.

C3one line summary

Stationary Navier-Stokes solutions in R^3 are trivial under L^{9/2 + ε(·)} integrability with ε(·)>0, and the condition suffices when imposed only at infinity.

Formal links

2 machine-checked theorem links

Cited by

2 papers in Pith

Notes on Liouville-type theorems for the 3D stationary Navier-Stokes equations

Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component

Receipt and verification

First computed	2026-05-22T01:04:01.651807Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8db28e536ef7aeda96a1493943a9a6bd8c6b49f6324211469a1167ef7384145c

Aliases

arxiv: 2604.06527 · arxiv_version: 2604.06527v2 · doi: 10.48550/arxiv.2604.06527 · pith_short_12: RWZI4U3O66XN · pith_short_16: RWZI4U3O66XNVFVB · pith_short_8: RWZI4U3O

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RWZI4U3O66XNVFVBJE4UHKNGXW \
  | 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: 8db28e536ef7aeda96a1493943a9a6bd8c6b49f6324211469a1167ef7384145c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "402b91fc997622941dfa9cfa0e48fb80cde3b4862eaabf69e878038f2817e5b9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-04-07T23:50:50Z",
    "title_canon_sha256": "982af4797f134f0842c681ea88c967ab0dcb1ff7a02c668ea59e31e06ee2154c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06527",
    "kind": "arxiv",
    "version": 2
  }
}