Pith Number

pith:UJAWGC5A

pith:2026:UJAWGC5AT2JXTH7O2D7IKPI752

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Spectral instability and non-uniqueness of mild solutions for the Keller-Segel system

Eliseo Luongo, Umberto Pappalettera

The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n from 3 to 9 and q in the supercritical range [1, n/2).

arxiv:2605.13592 v1 · 2026-05-13 · math.AP · math.SP

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Claims

C1strongest claim

We show that the Cauchy problem associated with the parabolic-elliptic Keller-Segel model is locally ill-posed in L^q(R^n) for dimensions n ∈ {3,…,9} and throughout the supercritical range q∈[1,n/2).

C2weakest assumption

The non-uniqueness is driven by an instability mechanism in self-similarity variables, assuming the spectral instability from the Jia-Šverák Navier-Stokes program transfers directly to the Keller-Segel linearization without extra obstructions.

C3one line summary

The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n=3..9 and supercritical q in [1, n/2).

References

46 extracted · 46 resolved · 0 Pith anchors

[1] Archive for Rational Mechanics and Analysis , VOLUME = 2016 · doi:10.1007/s00205-016-1017-8

[2] Journal of Functional Analysis , VOLUME = 2024 · doi:10.1016/j.jfa.2024.110541

[3] Geometric and Functional Analysis , VOLUME = 2025 · doi:10.1007/s00039-025-00706-0

[4] Annals of PDE , VOLUME = 2023 · doi:10.1007/s40818-023-00155-8

[5] Journal f\"ur die Reine und Angewandte Mathematik 2025 · doi:10.1515/crelle-2025-0025

Receipt and verification

First computed	2026-05-18T02:44:23.053536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a241630ba09e93799feed0fe853d1feebd35ebe6a53dccfe3ac7688d66e1f499

Aliases

arxiv: 2605.13592 · arxiv_version: 2605.13592v1 · doi: 10.48550/arxiv.2605.13592 · pith_short_12: UJAWGC5AT2JX · pith_short_16: UJAWGC5AT2JXTH7O · pith_short_8: UJAWGC5A

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752 \
  | 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: a241630ba09e93799feed0fe853d1feebd35ebe6a53dccfe3ac7688d66e1f499

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "776a23c53d173fab09784b88b51961b5a9075544b82d22520770ccab660205a0",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T14:26:28Z",
    "title_canon_sha256": "cc838549e3beda93ff314105ecf054f0e0215f3e390bee8f0f7b2d000b88d5fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13592",
    "kind": "arxiv",
    "version": 1
  }
}