{
  "abstract": "In this paper, we study a generalised family of fractional BBM equations on the $d$ dimensional torus $\\mathbb{T}^d$ for $d\\geq 1$. We establish low regularity local and global well-posedness results on the $H^s(\\mathbb{T}^d)$ scale that improve upon the works of Bona and Chen (2003) and Kim and Kwak (2026). We also prove endpoint global well-posedness for the cubic regularised Benjamin-Ono equation in $H^{1/2}(\\mathbb{T})$. Furthermore, we obtain a well-posedness result for the generalised fractional BBM in the spaces $L^{k+1}(\\mathbb{T}^d)$ where $k$ is order of the polynomial nonlinearity. As an application of this result, we show that for a certain range of values and for a suitable randomisation of the initial data, the model is almost surely globally well-posed in $H^s(\\mathbb{T}^d)$ for $s\\geq 0$. Lastly, we show that the family exhibits a strong form of ill-posedness in $H^s(\\mathbb{T}^d)$ for $s<0$ in the form of an infinite loss of regularity at all initial datum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03288",
  "author_total": 1,
  "authors": [
    {
      "name": "Jackson Barratt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zjsxt9mjtbfg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03288",
  "fulltext_url": null,
  "id": "4zjsxt9mjtbfg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03288",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7220472506",
  "pdf_url": "https://arxiv.org/pdf/2610.03288",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zjsxt9mjtbfg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03288",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03288"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Well-posedness for the generalised fractional BBM equation",
  "title_text": "Well-posedness for the generalised fractional BBM equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/4zjsxt9mjtbfg",
  "venue": "arXiv",
  "versions": []
}