{
  "abstract": "In this paper, we derive the rotation-two-component $b$-family shallow-water wave system from the Green--Naghdi type equations incorporating the effects of the Coriolis force and constant vorticity. The system admits, among its special cases, the two-component Degasperis--Procesi (2DP) system as a reduction, thereby confirming its genuine role as a rotational extension of the $b$-family. We then focus on a specific reduction, the rotation-two-component Degasperis-Procesi system, whose particular interest lies in the fact that it combines two independent sources of difficulty: unlike the two-component Camassa-Holm type system, it possesses no conserved $H^1\\times L^2$-type quantity, and in contrast to the standard 2DP system, it contains a higher-order nonlinear coupling term induced by the Coriolis force. To overcome this double difficulty, we introduce an auxiliary variable and establish a local $L^\\infty$-estimate for $u$ without using any conservation law, based on which we derive two distinct blow-up criteria. When the Coriolis force vanishes, our results recover known criteria for the 2DP system and also provide new criteria for both the 2DP system and Degasperis-Procesi equation. The results extend naturally to the periodic setting and to relevant special cases of the rotational $b$-family system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09900",
  "author_total": 1,
  "authors": [
    {
      "name": "Xingxing Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d41d4abtqsbtr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09900",
  "fulltext_url": null,
  "id": "d41d4abtqsbtr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09900",
  "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",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7212111448",
  "pdf_url": "https://arxiv.org/pdf/2609.09900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d41d4abtqsbtr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09900"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the rotation-two-component $b$-family shallow-water system: derivation and wave-breaking analysis",
  "title_text": "On the rotation-two-component b-family shallow-water system: derivation and wave-breaking analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/d41d4abtqsbtr",
  "venue": "arXiv",
  "versions": []
}