Pith Number

pith:C6EGP2TA

pith:2026:C6EGP2TAN4WAJGN2VMXMESCY6N

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On existence of local and global strong solutions for the stochastic tamed Navier-Stokes equations on $\mathbb{R}^3$

Bikram Podder, Surendra Kumar

Stochastic tamed Navier-Stokes equations on R^3 admit pathwise unique maximal local strong solutions for initial data in L^p with p greater than 3, and unique global solutions with added H^1 regularity.

arxiv:2605.03734 v2 · 2026-05-05 · math.AP · math.PR

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\pithnumber{C6EGP2TAN4WAJGN2VMXMESCY6N}

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3 Author claim open · sign in to claim

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 first prove the existence of a pathwise unique maximal local strong solution for F_0-measurable initial data in L^p(Ω; L^p(R^3; R^3)) for p > 3. Furthermore, by assuming initial data in L^p(Ω; L^p(R^3; R^3)) ∩ L^2(Ω; H^1(R^3; R^3)), we overcome the non-local pressure obstruction to establish the existence of a unique global strong solution.

C2weakest assumption

The initial data must satisfy the stated integrability conditions in L^p for p>3 (and additional H^1 regularity for the global case); the taming mechanism is assumed to be sufficient to control the nonlinearity and allow continuation past potential singularities.

C3one line summary

Pathwise unique maximal local strong solutions exist for initial data in L^p(Ω; L^p(R^3)) with p>3, and unique global strong solutions exist when initial data also lies in L^2(Ω; H^1(R^3)).

Receipt and verification

First computed	2026-06-02T03:05:05.590177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

178867ea606f2c0499baab2ec24858f363add366962ee547821a0d1a93718c09

Aliases

arxiv: 2605.03734 · arxiv_version: 2605.03734v2 · doi: 10.48550/arxiv.2605.03734 · pith_short_12: C6EGP2TAN4WA · pith_short_16: C6EGP2TAN4WAJGN2 · pith_short_8: C6EGP2TA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/C6EGP2TAN4WAJGN2VMXMESCY6N \
  | 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: 178867ea606f2c0499baab2ec24858f363add366962ee547821a0d1a93718c09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "938468e8e8e9ec726fd6d30f5c499482e49a5a70981f22e9db7f28f1e65b0db9",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-05T13:22:29Z",
    "title_canon_sha256": "a29b5c6985bbdb7daa55f5970d3f34b0bde711fee8559fe05590223f91249626"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03734",
    "kind": "arxiv",
    "version": 2
  }
}