{
  "abstract": "We prove global well-posedness and scattering for the three-dimensional defocusing cubic nonlinear Schrödinger equation with arbitrary initial data in $H^s(\\R^3)$, $s>\\frac{1}{2}$, without radial symmetry. The proof combines the $I$-method with long-time $L^2_{t,x}$ bounds for products of frequency-localized components of the nonlinear solution. The key high--low estimate follows from a directional interaction identity pairing high-frequency mass with low-frequency energy, together with an induction on frequency.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24830",
  "author_total": 2,
  "authors": [
    {
      "name": "Qingtang Su"
    },
    {
      "name": "Zehua Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e1dtdt92a92cp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24830",
  "fulltext_url": null,
  "id": "e1dtdt92a92cp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24830",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
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  ],
  "openalex": "W7214036622",
  "pdf_url": "https://arxiv.org/pdf/2609.24830",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e1dtdt92a92cp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.24830",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24830"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in $H^s$, $s>\\frac{1}{2}$",
  "title_text": "Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in H^s, s>1/2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/e1dtdt92a92cp",
  "venue": "arXiv",
  "versions": []
}