{
  "abstract": "We prove that the Benjamin-Bona-Mahony equation is almost surely globally well-posed with respect to random Gaussian initial data of negative Sobolev regularity in $H^{s}(\\mathbb{T})$ for any $s>-\\frac 14$. This result is sharp in view of the mild probabilistic ill-posedness due to Oh-Tzvetkov (2026). This also improves on a previous result of the author which established this only in a logarithmically negative regularity. To break through this logarithmic regularity barrier, we combine the $I$-method with the low-high argument from Bona-Tzvetkov (2007), which motivates a refined first-order expansion for solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36403",
  "author_total": 1,
  "authors": [
    {
      "name": "Justin Forlano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/916rhx3d1d7ss.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36403",
  "fulltext_url": null,
  "id": "916rhx3d1d7ss",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36403",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7214935290",
  "pdf_url": "https://arxiv.org/pdf/2609.36403",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/916rhx3d1d7ss.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36403",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36403"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Almost sure global well-posedness for the Benjamin-Bona-Mahony equation",
  "title_text": "Almost sure global well-posedness for the Benjamin-Bona-Mahony equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/916rhx3d1d7ss",
  "venue": "arXiv",
  "versions": []
}