{
  "abstract": "Let $U$ and $H$ be two separable Hilbert spaces and $T>0$. We consider a stochastic differential equation which evolves in the Hilbert space $H$ of the form \\begin{align} \\label{SDEa} dX(t)=AX(t)dt+B(t,X(t))dt+GdW(t), \\quad t\\in[0,T], \\quad X(0)=x \\in H, \\end{align} where $A:D(A)\\subseteq H\\to H$ is the infinitesimal generator of a strongly continuous semigroup $(e^{tA})_{t\\geq0}$, $W=(W(t))_{t\\geq0}$ is a $U$-cylindrical Wiener process defined on a normal filtered probability space $(Ω,\\mathcal{F},\\{\\mathcal{F}_t\\}_{t\\in [0,T]},\\mathbb{P})$, $G:U\\to H$ is a linear bounded operator and $B:[0,T]\\times H\\to H_β$ is a locally $θ$-Hölder continuous function with respect to the second variable, uniformly with respect to the first one, for some suitable $θ\\in(0,1)$. Here, $H_β$ is a Hilbert space which contains $H$ with continuous embedding, so that the drift term is singular: it is not well-defined from the ambient space $H$ into itself. The coefficient $β\\geq0$ measures the order of such a singularity and the case $β=0$ corresponds to a drift term with values in $H$. We prove that, under suitable assumptions on the coefficients, weak and pathwise uniqueness hold true for equation \\eqref{SDEa}. In particular, the conditions assumed on the coefficients cover the stochastic damped wave equation in dimension $1$ and the stochastic damped Euler--Bernoulli beam equation up to dimension $3$, even in the hyperbolic case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03819",
  "author_total": 2,
  "authors": [
    {
      "name": "Davide Addona"
    },
    {
      "name": "Davide Augusto Bignamini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bevwbp9q58ppb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03819",
  "fulltext_url": null,
  "id": "bevwbp9q58ppb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03819",
  "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.PR"
    ],
    [
      "openalex",
      "2604|Nonlinear Differential Equations Analysis"
    ]
  ],
  "openalex": "W7208786050",
  "pdf_url": "https://arxiv.org/pdf/2609.03819",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bevwbp9q58ppb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03819",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03819"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stochastic damped wave and Euler-Bernoulli equations with singular locally Hölder continuous drift",
  "title_text": "Stochastic damped wave and Euler-Bernoulli equations with singular locally Hölder continuous drift",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/bevwbp9q58ppb",
  "venue": "arXiv",
  "versions": []
}