{
  "abstract": "In this paper, we study the final data problem for the defocusing nonlinear Schrödinger equation (NLS) $$ i\\partial_t u + \\frac12Δu = |u|^p u $$ in weighted spaces $\\dotΣ^s(\\mathbb R^d):=L_x^2(\\mathbb R^d;|x|^{2s}\\mathrm{d} x)$. Let $s_c=\\frac d2-\\frac2p$. Under the scaling of the NLS, $\\dotΣ^{-s_c}(\\mathbb R^d)$ is the scaling-critical weighted space. In three dimensions, within the range of exponents considered in this paper, we show that the final data problem is locally well-posed for $s\\geq -s_c$ and ill-posed for $s<-s_c$. This is opposite to the corresponding initial data problem, which is locally well-posed for $s\\leq -s_c$ and ill-posed for $s>-s_c$. For the three-dimensional quadratic equation, we further obtain a unique global solution for every radial final datum in the critical space $\\dotΣ^{\\frac12}(\\mathbb R^3)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37785",
  "author_total": 4,
  "authors": [
    {
      "name": "Yujin Guo"
    },
    {
      "name": "Jia Shen"
    },
    {
      "name": "Yifei Wu"
    },
    {
      "name": "Changping Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3f5a1z45t1916.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37785",
  "fulltext_url": null,
  "id": "3f5a1z45t1916",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37785",
  "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": "W7214905955",
  "pdf_url": "https://arxiv.org/pdf/2609.37785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3f5a1z45t1916.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global theory for NLS in the weighted spaces II: final data problem",
  "title_text": "Global theory for NLS in the weighted spaces II: final data problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/3f5a1z45t1916",
  "venue": "arXiv",
  "versions": []
}