{
  "abstract": "We investigate the critical Reynolds number for the onset of long-wave instability in gravity-driven flows of generalized Newtonian fluids. A new factorized representation is derived, revealing the underlying structure of the problem and reducing the analysis to a small number of dimensionless quantities. This framework yields a universal lower bound valid for all admissible rheologies, together with several explicit upper and lower bounds. Sharper bounds are obtained for shear-thinning fluids in the presence of a yield stress. In the shear-thinning case, we establish an optimal universal upper bound. The optimal constant is attained in the Newtonian case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "François Rousset"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/64mj32d805jnq.bib",
  "cited_by": 0,
  "doi": "10.1007/s00033-026-02957-9",
  "fulltext_url": null,
  "id": "64mj32d805jnq",
  "issns": [
    "0044-2275",
    "1420-9039"
  ],
  "landing_url": "https://hal.science/hal-05838814v1",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.phys.mphy"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Thin Films"
    ]
  ],
  "openalex": "W7223318025",
  "pdf_url": "https://hal.science/hal-05838814/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "Springer Verlag",
  "ris": "https://research.draconitic.com/paper/64mj32d805jnq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05838814",
      "source": "hal",
      "url": "https://hal.science/hal-05838814v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.phys.mphy",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
    }
  ],
  "title": "On the structure of the critical Reynolds number for roll-wave instability in generalized Newtonian falling films",
  "title_text": "On the structure of the critical Reynolds number for roll-wave instability in generalized Newtonian falling films",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/64mj32d805jnq",
  "venue": "Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées",
  "versions": []
}