{
  "abstract": "The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. Well-posedness can however be recovered globally in time on a probabilistic level, provided the Fourier coefficients of the random initial data follow a sub-Gaussian law, an assumption on which the available proofs rely heavily. In this article we perform numerical simulations of the one dimensional fractional cubic defocusing wave equation in a periodic setting, with low regularity random initial data drawn either from a Gaussian or from a heavy tailed Student law. Besides illustrating probabilistic well-posedness and norm inflation in both the energy subcritical and supercritical regimes, our simulations display no qualitative difference between the heavy tailed and the sub-Gaussian cases. This leads us to conjecture that probabilistic well-posedness holds under the sole assumption that the Fourier coefficients are centered with finite variance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2604.05938",
  "author_total": 2,
  "authors": [
    {
      "name": "Wandrille Ruffenach"
    },
    {
      "name": "Nikolay Tzvetkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2q1n7827mgyb5.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "2q1n7827mgyb5",
  "issns": [],
  "landing_url": "https://hal.science/hal-05583261v2",
  "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.info"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05583261/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2q1n7827mgyb5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-05583261",
      "source": "hal",
      "url": "https://hal.science/hal-05583261v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Numerical study of probabilistic well-posedness of one dimensional fractional nonlinear wave equations",
  "title_text": "Numerical study of probabilistic well-posedness of one dimensional fractional nonlinear wave equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:27Z",
  "url": "https://research.draconitic.com/paper/2q1n7827mgyb5",
  "venue": "HAL",
  "versions": []
}