{
  "abstract": "We identify unstable radial equilibria as sharp concentration thresholds for the Jäger--Luckhaus chemotaxis system on the unit disk with no-flux boundary conditions. Concentration is compared through cumulative mass. At fixed total mass, every radial initial profile more concentrated than an unstable equilibrium produces finite-time blow-up, whereas every nonstationary profile less concentrated than that equilibrium generates a global, uniformly bounded solution converging to the least concentrated radial equilibrium. We also classify the radial equilibria and determine their nonlinear stability. Let $Λ= j_{1,1}^{2}$, where $j_{1,1}$ is the first positive zero of the Bessel function $J_1$. For $M\\ne Λπ$, the least concentrated equilibrium is the unique locally asymptotically stable equilibrium under mass-preserving radial perturbations. It is spatially homogeneous for $M<Λπ$ and strictly increasing for $M>Λπ$. Every other radial equilibrium, including the homogeneous state at $M=Λπ$, is nonlinearly unstable. These results clarify how total population and initial spatial aggregation jointly determine collapse or bounded redistribution, and how stable peripheral enrichment can occur within the radial model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39209",
  "author_total": 2,
  "authors": [
    {
      "name": "Xuan Mao"
    },
    {
      "name": "Wanwan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sawvffx1zzd6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39209",
  "fulltext_url": null,
  "id": "0sawvffx1zzd6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39209",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0sawvffx1zzd6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39209"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Unstable radial equilibria as sharp concentration thresholds for the Jäger--Luckhaus model on the unit disk",
  "title_text": "Unstable radial equilibria as sharp concentration thresholds for the Jäger--Luckhaus model on the unit disk",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0sawvffx1zzd6",
  "venue": "arXiv",
  "versions": []
}