{
  "abstract": "This work is devoted to the study of the hydrodynamic limit for the fluid-particle flows governed by the Vlasov-Fokker-Planck (VFP) equation coupled with the incompressible Navier-Stokes (INS) equation as the Deborah number approaches to zero. The limit is valid globally in time provided that the initial perturbation is small in a neighborhood of a steady state. The proof is based on a formal derivation of the limiting system via the Hilbert approach, followed by a rigorous justification via introducing a novel decomposition involving some macroscopic quantities and a refined energy estimate motivated by macro-micro decomposition. In contrast to the existing results for the same scaled model, the present work provides the first one on the hydrodynamic limits in a strong sense with an explicit convergence rate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Math. Models Methods Appl. Sci. 34 (2024), no. 12, 2265-2304",
  "arxiv": "2610.39204",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhendong Fang"
    },
    {
      "name": "Kunlun Qi"
    },
    {
      "name": "Huanyao Wen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e5y6j346bnxas.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39204",
  "fulltext_url": null,
  "id": "e5y6j346bnxas",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39204",
  "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/2610.39204",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e5y6j346bnxas.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39204",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39204"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The small Deborah number limit for the fluid-particle flows: incompressible case",
  "title_text": "The small Deborah number limit for the fluid-particle flows: incompressible case",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/e5y6j346bnxas",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1142/s0218202524500489",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}