{
  "abstract": "We investigate the zero-noise limit for SDE's driven by Brownian motion with a divergence-free drift singular at the initial time and prove that a unique probability measure concentrated on the integral curves of the drift is selected. More precisely, we prove uniqueness of the zero-noise limit for divergence-free drifts in $L^1_{loc} ((0, T ];BV(\\mathbb{T}^d;\\mathbb{R}^d))\\cap L^q((0,T);L^p(\\mathbb{T}^d;\\mathbb{R}^d))$ where p and q satisfy a Prodi-Serrin condition. The vector field constructed by Depauw lies in this class and we show that for almost every initial datum, the zero-noise limit selects a probability measure concentrated on several distinct integral curves of this vector field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Jules Pitcho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ddkq0w8q5yx2.bib",
  "cited_by": 0,
  "doi": "10.1007/s00030-025-01140-9",
  "fulltext_url": null,
  "id": "5ddkq0w8q5yx2",
  "issns": [
    "1021-9722",
    "1420-9004"
  ],
  "landing_url": "https://hal.science/hal-05756979v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
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      "hal",
      "1.math.math-pr"
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      "openalex",
      "2604|Navier-Stokes equation solutions"
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  "openalex": "W4415049786",
  "pdf_url": "https://hal.science/hal-05756979/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": "Springer Verlag",
  "ris": "https://research.draconitic.com/paper/5ddkq0w8q5yx2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
      "native_id": "hal-05756979",
      "source": "hal",
      "url": "https://hal.science/hal-05756979v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-pr",
      "subfield": "probability"
    }
  ],
  "title": "On the zero-noise limit for SDE’s singular at the initial time",
  "title_text": "On the zero-noise limit for SDE’s singular at the initial time",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:37Z",
  "url": "https://research.draconitic.com/paper/5ddkq0w8q5yx2",
  "venue": "Nonlinear Differential Equations and Applications",
  "versions": []
}