{
  "abstract": "The parabolic-elliptic Keller-Segel system \\[ \\left\\{ \\begin{array}{l} u_t = Δu - \\nabla \\cdot (u\\nabla v), \\\\[1mm] 0 = Δv - μ+ u, \\qquad μ:=\\frac{1}{|Ω|} \\int_Ωu, \\end{array} \\right. \\qquad \\qquad (\\star) \\] is considered under homogeneous Neumann boundary conditions in the ball $Ω=B_R(0)\\subset {\\mathbb R}^n$, where $n\\ge 2$ and $R>0$. The main results identify a mass level $m_\\star(n,R)>0$ as critical in the sense that $\\bullet$ whenever $0<m<m_\\star(n,R)$, the constant equilibrium of ($\\star$) given by $u\\equiv v\\equiv \\frac{m}{|B_R|}$ is locally asymptotically stable with respect to the norm in $L^\\infty(B_R)$, but that $\\bullet$ if $m>m_\\star(n,R)$, then any solution of ($\\star$) emanating from nonnegative and nonconstant continuous radial initial data $u_0$ with $\\int_{B_R} u_0=m$ and $\\frac{1}{|B_r|} \\int_{B_r} u_0 \\ge \\frac{m}{|B_R|}$ for all $r\\in (0,R)$ blows up in finite time. The value of $m_\\star(n,R)$ can be determined in an essentially explicit manner in dependence on principal zeroes of appropriate Bessel functions of the first kind; in particular, $m_\\star(2,R)\\approx 14.68197 \\cdot π$ for all $R>0$. Accordingly, as a supplement to known mass-dependent blow-up dichotomies these findings reveal a genuinely secondary critical mass phenomenon for ($\\star$) especially also in its two-dimensional version in which no precedent of this form seems known.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13559",
  "author_total": 2,
  "authors": [
    {
      "name": "Yulan Wang"
    },
    {
      "name": "Michael Winkler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a37p9f939c0ev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13559",
  "fulltext_url": null,
  "id": "a37p9f939c0ev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13559",
  "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"
    ],
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      "openalex",
      "2611|Mathematical Biology Tumor Growth"
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  "openalex": "W7221550862",
  "pdf_url": "https://arxiv.org/pdf/2610.13559",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a37p9f939c0ev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13559",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13559"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Identifying secondary critical mass levels in two- and higher-dimensional Keller-Segel systems",
  "title_text": "Identifying secondary critical mass levels in two- and higher-dimensional Keller-Segel systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/a37p9f939c0ev",
  "venue": "arXiv",
  "versions": []
}