{
  "abstract": "We study a log-Hardy-Littlewood-Sobolev (log-HLS) inequality under constraints and a naturally induced Wasserstein flow. The constrained log-HLS inequality is dual, in a variational sense, to the constrained Trudinger-Moser-Onofri-Aubin inequality. The corresponding gradient-flow formulation leads to a parabolic-elliptic Patlak-Keller-Segel (PKS) system whose global dynamics exhibit a dichotomy between global existence and finite-time blow-up depending on the initial mass. Remarkably, the constraint raises the critical mass threshold of the flow by a factor of two compared with the unconstrained setting. This provides a distinct mechanism for suppressing blow-up from those arising in related formulations of the PKS-system, where blow-up is mitigated through additional effects such as a forcing term, coupling with a fluid equation, or the ambient flow generated by harmonic perturbations of the Newtonian potential.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05356",
  "author_total": 4,
  "authors": [
    {
      "name": "Monideep Ghosh"
    },
    {
      "name": "Debabrata Karmakar"
    },
    {
      "name": "Reetaj Sinha"
    },
    {
      "name": "Kartikey Verma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fv6vb5yve9nne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05356",
  "fulltext_url": null,
  "id": "fv6vb5yve9nne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05356",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7220659455",
  "pdf_url": "https://arxiv.org/pdf/2610.05356",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fv6vb5yve9nne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.05356",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05356"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A constrained log-HLS inequality and its associated Wasserstein flow",
  "title_text": "A constrained log-HLS inequality and its associated Wasserstein flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/fv6vb5yve9nne",
  "venue": "arXiv",
  "versions": []
}