{
  "abstract": "We prove global well-posedness and modified scattering for the three-dimensional Hartree equation for small data in $H^{0,k}$, with $k>\\frac12$ on $\\mathbb R^3$ and $k=1$ on the half-space $\\mathbb R^3_+$ with a real Robin boundary condition. For these data, the nonlinear and asymptotic analysis is carried out entirely in physical space, combining slow-growth estimates for Galilean vector fields with a scale-invariant interaction estimate. For the half-space problem, we construct an extension intertwining the Robin and free flows and a boundary-adapted field that overcome the loss of normal Galilean symmetry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21002",
  "author_total": 2,
  "authors": [
    {
      "name": "Benoît Pausader"
    },
    {
      "name": "Mengyi Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48vnvzw22jhrn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21002",
  "fulltext_url": null,
  "id": "48vnvzw22jhrn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21002",
  "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": "W7222527607",
  "pdf_url": "https://arxiv.org/pdf/2610.21002",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48vnvzw22jhrn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21002",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21002"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Physical-Space Approach to Modified Scattering for the 3D Hartree Equation: Full-Space and Robin Half-Space",
  "title_text": "A Physical-Space Approach to Modified Scattering for the 3D Hartree Equation: Full-Space and Robin Half-Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/48vnvzw22jhrn",
  "venue": "arXiv",
  "versions": []
}