{
  "abstract": "It is well known that solutions to deterministic Keller--Segel chemotaxis systems can blow up in finite time under certain conditions. To investigate whether noise can prevent such blow-up, we study parabolic--elliptic and fully parabolic Keller--Segel systems on smooth bounded domains with pointwise superlinear multiplicative Itô noise $σ_0u^r\\,\\mathrm dW_t$, where $W$ is a real Brownian motion. Our results show that superlinear multiplicative noise can prevent finite-time blow-up in Keller--Segel systems. For $r>3/2$, we prove global existence and pathwise uniqueness of nonnegative mild solutions in arbitrary spatial dimension, for every $σ_0>0$. At $r=3/2$, both systems are globally well-posed in two dimensions for every positive noise intensity; in arbitrary dimension, the parabolic--elliptic system is global under $σ_0^2\\ge2χ$. For $r>3/2$ in the fully parabolic case, the proof combines a logarithmic estimate for the time derivative of the chemical signal with comparison of the local solution to the solution of a scalar stochastic differential equation. The two-dimensional case follows from mass quadratic variation, deterministic maximal regularity, and localized energy estimates. We also establish almost-sure $L^1$ extinction and algebraic decay of fractional mass moments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36485",
  "author_total": 2,
  "authors": [
    {
      "name": "Yunfeng Chen"
    },
    {
      "name": "Tusheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hc7f6rheccgy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36485",
  "fulltext_url": null,
  "id": "4hc7f6rheccgy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36485",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2611|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7224085994",
  "pdf_url": "https://arxiv.org/pdf/2610.36485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hc7f6rheccgy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Global Well-posedness and Asymptotic Extinction for Keller-Segel Systems with Superlinear Noise",
  "title_text": "Global Well-posedness and Asymptotic Extinction for Keller-Segel Systems with Superlinear Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/4hc7f6rheccgy",
  "venue": "arXiv",
  "versions": []
}