{
  "abstract": "We extend the paracontrolled distribution approach of Gubinelli, Imkeller, and Perkowski to singular stochastic heat equations with Caputo fractional time derivatives. By establishing Schauder estimates for the time-fractional heat flow and controlling history terms, we address the difficulties arising from temporal memory and the lack of the semigroup property. For the one-dimensional rough Burgers-type equation driven by space-time white noise with spatial dissipation \\((-Δ)^σ\\), we prove global well-posedness for \\(σ\\in(5/6,1]\\) and \\(ν\\in(6σ/(12σ-5),1]\\). For the heat equation with nonlinear multiplicative spatial white noise on the two-dimensional torus, we establish local well-posedness of renormalized solutions and an \\(L^\\infty\\) blow-up criterion for every \\(ν\\in(0,1]\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23189",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuolin Zhang"
    },
    {
      "name": "\\quad Zhaoyang Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ykhpqr9034yt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23189",
  "fulltext_url": null,
  "id": "5ykhpqr9034yt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23189",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7222954462",
  "pdf_url": "https://arxiv.org/pdf/2610.23189",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ykhpqr9034yt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23189",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23189"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Singular Stochastic Heat Equations with Fractional Memory",
  "title_text": "Singular Stochastic Heat Equations with Fractional Memory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/5ykhpqr9034yt",
  "venue": "arXiv",
  "versions": []
}