Pith Number

pith:W4CBVMNY

pith:2026:W4CBVMNYT4L7XUGVRAYVXSICEP

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Well-posedness of a generalized Stokes operator on domains with cylindrical ends via layer-potentials

Mirela Kohr, Victor Nistor, Wolfgang Wendland

Under positivity assumptions on V and V0 the generalized Stokes operator Ξ and its layer potentials become invertible on domains with cylindrical ends.

arxiv:2605.10849 v2 · 2026-05-11 · math.AP · math-ph · math.DG · math.FA · math.MP

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Record completeness

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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

Under slightly stronger assumptions on V and V0, we prove the invertibility of the operators Ξ, S, and ½ + K. The invertibility of these operators leads to well-posedness results for the associated (linear) Stokes boundary value problem with Dirichlet boundary conditions on Ω. As an application, we prove the well-posedness result for the Dirichlet problem for the generalized Navier-Stokes system with small data on a domain with cylindrical ends.

C2weakest assumption

Under suitable positivity assumptions on V and V0, we prove that Ξ is Fredholm. Under further positivity assumptions, we prove that S and ½ + K are also Fredholm. Under slightly stronger assumptions on V and V0, we prove the invertibility...

C3one line summary

A generalized Stokes operator on cylindrical-end domains is Fredholm and invertible under positivity assumptions on V and V0 via layer potentials, yielding well-posedness for linear Stokes and small-data Navier-Stokes Dirichlet problems.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-29T02:05:46.414071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7041ab1b89f17fbd0d588315bc90223ee4bd70bb9a5f11b091b652702b0cefe

Aliases

arxiv: 2605.10849 · arxiv_version: 2605.10849v2 · doi: 10.48550/arxiv.2605.10849 · pith_short_12: W4CBVMNYT4L7 · pith_short_16: W4CBVMNYT4L7XUGV · pith_short_8: W4CBVMNY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W4CBVMNYT4L7XUGVRAYVXSICEP \
  | 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: b7041ab1b89f17fbd0d588315bc90223ee4bd70bb9a5f11b091b652702b0cefe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c48f9d673bec10a544cb96e9d8a6a4153d643a8600c486b53b8c1589fbef4e7a",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-11T16:59:02Z",
    "title_canon_sha256": "18e568f8a6096c1141cc6acd903a0488197b1b9ef4ab7048700d6b624dbaa1c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10849",
    "kind": "arxiv",
    "version": 2
  }
}