{
  "abstract": "Since Strain's work \\cite{Strain-2012-KRM} on almost optimal time decay rates for the microscopic part of perturbative classical solutions to the Boltzmann system with soft potentials via the time-velocity splitting method, how to obtain the optimal decay of the microscopic part has remained unsolved. In this paper, we resolve this problem by developing a nonlinear energy estimate method different from the time-velocity splitting approach. The proof relies on a combination of a hierarchy of time-weighted energy estimates, the damping factor \\(e^{-ν(v)(t-τ)}\\), and a dyadic decomposition of velocity space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32296",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuanjie Lei"
    },
    {
      "name": "Xiongju Wei"
    },
    {
      "name": "Tong Yang"
    },
    {
      "name": "Huijiang Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/awfy8v92sgq1f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32296",
  "fulltext_url": null,
  "id": "awfy8v92sgq1f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32296",
  "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": "W7223671832",
  "pdf_url": "https://arxiv.org/pdf/2610.32296",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/awfy8v92sgq1f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32296",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32296"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Optimal time decay of the Boltzmann equation with cutoff soft potentials in the whole space",
  "title_text": "Optimal time decay of the Boltzmann equation with cutoff soft potentials in the whole space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/awfy8v92sgq1f",
  "venue": "arXiv",
  "versions": []
}