{
  "abstract": "We prove a long time well-posedness result for a quadratic non-linear Schrödinger equation with random well prepared initial conditions in dimension d ≥ 1. In some regimes, we derive the Wave Kinetic equation associated with the equation in dimension d ≥ 5, almost up to the kinetic time to the power d/(d + 1). Our analysis relies on the ideas introduced by Deng and Hani.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28093",
  "author_total": 1,
  "authors": [
    {
      "name": "Enguerrand Brun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9pvm2ccggf0ky.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28093",
  "fulltext_url": null,
  "id": "9pvm2ccggf0ky",
  "issns": [],
  "landing_url": "https://hal.science/hal-05760949v2",
  "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": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
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      "hal",
      "0.math"
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    [
      "hal",
      "1.math.math-ap"
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    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
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  "openalex": "W7214182234",
  "pdf_url": "https://hal.science/hal-05760949/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9pvm2ccggf0ky.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:55Z",
      "native_id": "hal-05760949",
      "source": "hal",
      "url": "https://hal.science/hal-05760949v2"
    },
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.28093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28093"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Long time well-posedness and wave turbulence limit for a quadratic non-lienar Schrödinger equation with well prepared random initial data.",
  "title_text": "Long time well-posedness and wave turbulence limit for a quadratic non-lienar Schrödinger equation with well prepared random initial data.",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/9pvm2ccggf0ky",
  "venue": "HAL",
  "versions": []
}