{
  "abstract": "We establish global well-posedness near vacuum for the relativistic Boltzmann equation with soft and hard potentials in the range $γ\\in(-2,1]$. The initial data have critical Besov regularity of order $2/r$ in the transverse spatial variables for an admissible range of $r$ depending on $γ$, together with weighted integrability in the longitudinal and momentum variables. The proof combines a fixed-direction div--curl lemma with bilinear collision estimates. In particular, to control the gain term, we combine localization to spherical caps with energy-weighted angular estimates. The key relativistic estimate controls the singularity associated with the first component of the post-collisional relative velocity. These bounds yield the required time decay.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40322",
  "author_total": 4,
  "authors": [
    {
      "name": "Xinfeng Hu"
    },
    {
      "name": "Shuangqian Liu"
    },
    {
      "name": "Haoran Peng"
    },
    {
      "name": "Yi Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4kxxmjg4v8n15.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40322",
  "fulltext_url": null,
  "id": "4kxxmjg4v8n15",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40322",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40322",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4kxxmjg4v8n15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40322",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40322"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Relativistic collision geometry and global near-vacuum solutions at critical transverse regularity",
  "title_text": "Relativistic collision geometry and global near-vacuum solutions at critical transverse regularity",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4kxxmjg4v8n15",
  "venue": "arXiv",
  "versions": []
}