{
  "abstract": "We justify the hydrodynamic limit of the Vlasov-Fokker-Planck equation coupled with the incompressible Navier--Stokes equation in the fine regime with a quantitative convergence rate. In this regime, the limiting dynamics is described by the inhomogeneous incompressible Navier-Stokes system for the fluid-particle mixture. In contrast with the existing relative entropy approaches, the present work extends to a pointwise convergence of the hydrodynamic limits with an explicit rate on any given time interval [0,T]. The proof is based on a Macro-Micro decomposition around the moving local Maxwellian, together with an $\\varepsilon$-weighted energy-dissipation structure adapted to the fine particle relaxation scales. Furthermore, we remove the classical small background restriction inherent in high-order energy methods, allowing the limiting profile to be possibly large. This is accomplished by exploiting a hidden Kelvin-Voigt type damped wave equation structure within the macroscopic velocity error system, yielding the critical extra dissipation required to close the uniform estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21119",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhendong Fang"
    },
    {
      "name": "Jian Li"
    },
    {
      "name": "Kunlun Qi"
    },
    {
      "name": "Huanyao Wen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/atj9jqqczxfgb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21119",
  "fulltext_url": null,
  "id": "atj9jqqczxfgb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21119",
  "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",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7222476405",
  "pdf_url": "https://arxiv.org/pdf/2610.21119",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/atj9jqqczxfgb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21119",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21119"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Quantitative Hydrodynamic Limit for the Vlasov-Fokker-Planck/Navier-Stokes System in the Fine Particle Regime",
  "title_text": "A Quantitative Hydrodynamic Limit for the Vlasov-Fokker-Planck/Navier-Stokes System in the Fine Particle Regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/atj9jqqczxfgb",
  "venue": "arXiv",
  "versions": []
}