{
  "abstract": "While unconditional uniqueness for the cubic nonlinear Schrödinger equation (NLS) on $\\Bbb R^3$ is known in the scaling-subcritical Sobolev spaces $\\dot H^s(\\Bbb R^3)$ for $1/2<s<1$, the critical case $s=1/2$ has remained open. We resolve this problem by adapting Kato's bootstrap argument to the critical space $\\dot B^{-1}_{\\infty,\\infty}$. The main difficulty at this endpoint is that the natural solution class does not provide the coefficient regularity required to close the bootstrap in $\\dot B^{-1}_{\\infty,\\infty}$. To overcome this issue, we perform a second Duhamel iteration of Born type and estimate the resulting double Duhamel integral as a whole. This yields improved estimates that allow the bootstrap to close in $\\dot B^{-1}_{\\infty,\\infty}$ using only the available regularity of the coefficients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06501",
  "author_total": 2,
  "authors": [
    {
      "name": "Yongming Luo"
    },
    {
      "name": "Jiayu Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mf18r1hbh97p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06501",
  "fulltext_url": null,
  "id": "8mf18r1hbh97p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06501",
  "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"
    ]
  ],
  "openalex": "W7220729148",
  "pdf_url": "https://arxiv.org/pdf/2610.06501",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mf18r1hbh97p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.06501",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06501"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Unconditional uniqueness for the cubic nonlinear Schrödinger equation in $\\dot{H}^{\\frac12}(\\Bbb R^3)$",
  "title_text": "Unconditional uniqueness for the cubic nonlinear Schrödinger equation in Ḣ^1/2(Bbb R^3)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/8mf18r1hbh97p",
  "venue": "arXiv",
  "versions": []
}