{
  "abstract": "In this paper, we establish quantitative Darcy limits for a three-dimensional inhomogeneous incompressible fluid with temperature-dependent viscosity and quasi-static thermal feedback. The domain is either the flat torus or a bounded domain with $C^{3,β}$ boundary, $0<β<1$. The holes have size $\\varepsilon^α$ and separation of order $\\varepsilon$, with $1<α<3$. Before normalization, the fluid and solid conductivities are $σ_\\varepsilon^2κ_f$ and $σ_\\varepsilon^2κ_s$, where $σ_\\varepsilon^2\\sim\\varepsilon^{3-α}$. This scaling preserves the thermal feedback in the limit. For a sufficiently regular reference solution and under an explicit absorption condition, the squared density, velocity and temperature errors are bounded by the weighted initial discrepancy together with $\\varepsilon^{α-1}+\\varepsilon^{3-α}$ on the torus and $\\varepsilon^{α-1}+\\varepsilon^{(3-α)/2}$ in a bounded domain. An interface-independent temperature estimate controls the viscosity discrepancy, and a weighted Stokes residual retains the coefficient and cell-pressure commutators. The bounded comparison uses a solenoidal wall correction and cellwise divergence repair. We also construct fixed-parameter microscopic weak solutions. The local strong effective solutions require a separate contraction condition in both settings and stronger boundary regularity in the bounded case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09528",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiaojiao Pan"
    },
    {
      "name": "Luqi Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/akfhncyhgk817.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09528",
  "fulltext_url": null,
  "id": "akfhncyhgk817",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09528",
  "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",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W7221006642",
  "pdf_url": "https://arxiv.org/pdf/2610.09528",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/akfhncyhgk817.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09528",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09528"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative thermoviscous Darcy limits in periodic and bounded domains",
  "title_text": "Quantitative thermoviscous Darcy limits in periodic and bounded domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/akfhncyhgk817",
  "venue": "arXiv",
  "versions": []
}