{
  "abstract": "We establish the local well-posedness of strong solutions for a thermodynamically consistent diffuse interface model describing two-phase flows with surfactants, specifically the so-called Model C introduced by Garcke, Lam, and Stinner. Because of the non-standard, mixed-order strongly coupled structure of Model C, the classical Agmon-Douglis-Nirenberg theory and conventional Lopatinskii-Shapiro boundary conditions are not applicable due to divergent scaling behaviors. To overcome this, we develop a tailored resolvent analysis, adapted to the temporal regularity of the source term, in a suitable Hilbert space, which yields an exact cancellation of the highest-order cross-couplings in the estimates. This crucial decoupling enables the rigorous application of the operator-valued Mikhlin multiplier theorem to obtain resolvent estimates on $\\mathbb{R}$. Furthermore, we analyze a structural variant, denoted as Model D, which achieves a crucial structural decoupling by transferring the interfacial surfactant energy entirely from the gradient part to the potential part, and we readily establish local well-posedness for strong solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03342",
  "author_total": 2,
  "authors": [
    {
      "name": "Helmut Abels"
    },
    {
      "name": "Songzhuang Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/315xehqdypnf4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03342",
  "fulltext_url": null,
  "id": "315xehqdypnf4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03342",
  "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": "W7220444310",
  "pdf_url": "https://arxiv.org/pdf/2610.03342",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/315xehqdypnf4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03342",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03342"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Local Well-posedness of a Diffuse Interface Two-phase Flow Model with Surfactants",
  "title_text": "Local Well-posedness of a Diffuse Interface Two-phase Flow Model with Surfactants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/315xehqdypnf4",
  "venue": "arXiv",
  "versions": []
}