{
  "abstract": "The Navier-Stokes/Mean Curvature Flow system describes a two-phase flow of incompressible, viscous and immiscible fluids separated by a sharp interface, whose evolution is governed by a convective mean curvature flow equation, coupled to a two-phase Navier-Stokes equation accounting for surface tension. Among others, this model describes the dynamics of dry foams and it also arises as a sharp interface limit of Navier-Stokes/Allen-Cahn systems with non-vanishing mobility. Despite this wide range of applications, global-in-time existence of any kind of weak solutions remains a challenging open problem. In this work, we introduce a novel notion of varifold weak solution in two and three ambient dimensions, based on a sharp energy dissipation principle à la De Giorgi, and we show for the first time the unconditional global-in-time existence of such a weak solution. We also show, by means of a relative entropy approach, that any classical solution to the Navier-Stokes/Mean Curvature Flow system is unique in the class of our new weak varifold solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00732",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Poiatti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dh0ydam4aayd5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00732",
  "fulltext_url": null,
  "id": "dh0ydam4aayd5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00732",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7215790417",
  "pdf_url": "https://arxiv.org/pdf/2610.00732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dh0ydam4aayd5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Global weak varifold solutions to Navier-Stokes/Mean Curvature Flow system",
  "title_text": "Global weak varifold solutions to Navier-Stokes/Mean Curvature Flow system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/dh0ydam4aayd5",
  "venue": "arXiv",
  "versions": []
}