{
  "abstract": "This note gives a complete classification of the asymptotic behavior of radial solutions to the two-dimensional parabolic-elliptic Keller-Segel system on the whole space, for general initial data in the large. We review previous separate results, and unify them within a single classification framework. Depending on the mass, the flow exhibits three distinct asymptotic regimes. For a subcritical mass, solutions converge toward the unique self-similar expander of same mass. At the critical mass 8π, solutions concentrate in infinite time around the stationary state with a universal logarithmic rate. The determination of this behaviour was the last missing step for achieving a complete radial classification, and we prove it in a companion paper (in fact without radial assumption). For a supercritical mass, solutions undergo type II finite-time blow-up with an explicit universal asymptotic rate and the stationary state as profile. This trichotomy holds for all radial initial data with finite second momentum. For non-radial data or infinite second momentum, it is known that other dynamics can be possible; for each of these three universal regimes we review the known results showing how they persist.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.20870",
  "author_total": 2,
  "authors": [
    {
      "name": "Federico Buseghin"
    },
    {
      "name": "Charles Collot"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgz94n3bkf4vb.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "cgz94n3bkf4vb",
  "issns": [],
  "landing_url": "https://hal.science/hal-05781866v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05781866/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cgz94n3bkf4vb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:49Z",
      "native_id": "hal-05781866",
      "source": "hal",
      "url": "https://hal.science/hal-05781866v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "CLASSIFICATION OF THE DYNAMICS OF RADIAL SOLUTIONS TO THE 2D PARABOLIC-ELLIPTIC KELLER-SEGEL SYSTEM",
  "title_text": "CLASSIFICATION OF THE DYNAMICS OF RADIAL SOLUTIONS TO THE 2D PARABOLIC-ELLIPTIC KELLER-SEGEL SYSTEM",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:49Z",
  "url": "https://research.draconitic.com/paper/cgz94n3bkf4vb",
  "venue": "HAL",
  "versions": []
}