{
  "abstract": "We establish a conditional theory of genuinely non-perturbative global dynamics for the cutoff Boltzmann equation with hard potentials on the three-dimensional torus. We prove that any global mild solution satisfying \\[ \\sup_{t\\ge0}\\int_{\\mathbb R^3}W(v)\\sup_{x\\in\\mathbb T^3}F(t,x,v)\\,dv<\\infty, \\] for a suitable stretched-exponential weight \\(W\\), enjoys uniform weighted \\(L^\\infty\\) control, is unique in the dissipative mild class, and converges exponentially to the global Maxwellian. In particular, these conclusions hold for arbitrary-amplitude solutions admitting a uniform stretched-exponential velocity upper bound. The key mechanism is a *tail-to-coercivity principle*: uniform velocity-tail control generates positive lower bounds for the local density and nonlinear collision frequency, without imposing macroscopic coercivity a priori. A double-Duhamel positivity argument also generates a Gaussian lower bound at arbitrarily short positive times, allowing initial data with local vacuum. We establish a polynomially weighted counterpart under an additional spatially uniform lower velocity profile, obtaining analogous weighted \\(L^\\infty\\) bounds, uniqueness, and exponential relaxation. Our results provide a low-regularity alternative to conditional theories requiring smoothness and pointwise macroscopic bounds. They reveal how a single velocity-tail condition controls large-data Boltzmann dynamics and suggest a route toward problems with physical boundary conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12093",
  "author_total": 5,
  "authors": [
    {
      "name": "Lingbing He"
    },
    {
      "name": "Jin-Cheng Jiang"
    },
    {
      "name": "Jong-In Kim"
    },
    {
      "name": "Donghyun Lee"
    },
    {
      "name": "Sungbin Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4qps7bxq8hzj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12093",
  "fulltext_url": null,
  "id": "d4qps7bxq8hzj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12093",
  "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"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7221085460",
  "pdf_url": "https://arxiv.org/pdf/2610.12093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4qps7bxq8hzj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12093"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Kinetic Concentration criterion for Large-data Boltzmann Dynamics",
  "title_text": "A Kinetic Concentration criterion for Large-data Boltzmann Dynamics",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d4qps7bxq8hzj",
  "venue": "arXiv",
  "versions": []
}