{
  "abstract": "Although there are many important contributions on compressible and incompressible fluid-particle interaction models respectively, how to connect the two-type fluid-particle models via the low Mach number limit remains a challenging open problem. In this paper, we resolve it for the compressible isentropic fluid-particle model (Euler--Vlasov--Fokker--Planck (Euler--VFP) system) in the whole space $\\mathbb{R}^3$. First, we establish the global-in-time {\\it a priori estimates} of strong solutions that are uniform with respect to the Mach number $\\varepsilon$ near the global Maxwellian. The proof relies on a refined energy method that combines the relaxation structure $b^\\varepsilon-u^\\varepsilon$ induced by the fluid-particle interaction and the symmetrized acoustic structure of the compressible Euler part in the model. Under the assumption of well-prepared initial data, we derive a {\\it global-in-time} uniform error estimate in the $H^2$ framework between the solution of the compressible Euler--VFP system and that of the limiting incompressible Euler--VFP system. A key point is to introduce the corrected acoustic variable $ q^\\varepsilon-\\varepsilon [P'(1)]^{-1}π$, which captures the pressure corrector in the low Mach number limit. This also allows us to exploit the exact cancellation of the singular acoustic terms and to close the {\\it global-in-time} error estimate. The damping term $b^\\varepsilon-u^\\varepsilon$, which is absent in the pure Euler equations, plays an essential role in recovering the relative velocity dissipation and in controlling the coupled fluid-particle dynamics. As a consequence, we prove the low Mach number limit of the compressible Euler--VFP system with the convergence rate $\\mathcal O(\\varepsilon)$ in the time-continuous $H^2$ topology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12648",
  "author_total": 3,
  "authors": [
    {
      "name": "Fucai Li"
    },
    {
      "name": "Jinkai Ni"
    },
    {
      "name": "Zhipeng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5j8pnfnen9g68.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12648",
  "fulltext_url": null,
  "id": "5j8pnfnen9g68",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12648",
  "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|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7212597349",
  "pdf_url": "https://arxiv.org/pdf/2609.12648",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5j8pnfnen9g68.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12648",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12648"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Low Mach number limit of the compressible Euler--Vlasov--Fokker--Planck system in the whole space",
  "title_text": "Low Mach number limit of the compressible Euler--Vlasov--Fokker--Planck system in the whole space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/5j8pnfnen9g68",
  "venue": "arXiv",
  "versions": []
}