{
  "abstract": "We study the initial-boundary value problem for the Cahn-Hilliard equation with degenerate mobility and singular diffusion at pure phases. This model describes the dynamics of phase separation in polymer blends with associated Flory-Huggins-de Gennes free energy. We prove the existence of global weak solutions in three-dimensional bounded and smooth domains, assuming that the initial datum has finite energy. We show the classical regularity in $L^2(0,T;H^2(Ω))$ for both the solution $u$ and the function $ϕ(u)=\\arcsin(u)$ through entropy estimates. In addition, when $Ω$ is convex, a new elliptic-type argument yields the refined regularity $u, ϕ(u) \\in L^4(0,T; H^2(Ω))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06371",
  "author_total": 3,
  "authors": [
    {
      "name": "Monica Conti"
    },
    {
      "name": "Andrea Giorgini"
    },
    {
      "name": "Greta Ricchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/35xanw3ajs9zj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06371",
  "fulltext_url": null,
  "id": "35xanw3ajs9zj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06371",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2505|Solidification and crystal growth phenomena"
    ]
  ],
  "openalex": "W7201855923",
  "pdf_url": "https://arxiv.org/pdf/2608.06371",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/35xanw3ajs9zj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2608.06371",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06371"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global weak solutions to the Cahn-Hilliard equation with degenerate mobility and singular diffusion",
  "title_text": "Global weak solutions to the Cahn-Hilliard equation with degenerate mobility and singular diffusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/35xanw3ajs9zj",
  "venue": "arXiv",
  "versions": []
}