{
  "abstract": "We study the two-dimensional quadratic Schrödinger equation $(i\\partial_t+Δ)u=λ_1u^2+λ_2\\overline u^{\\,2}$ with initial data of size $\\varepsilon$ in a weighted $H^2$ space. We prove almost global existence, with a lifespan of at least $\\exp(c/\\varepsilon)$ and decay at the optimal linear dispersive rate $t^{-1}$. Our proof is based on the space--time resonance method introduced by Germain, Masmoudi, and Shatah. The main new ingredient is a Besov-type profile norm $\\mathcal Z$, which allows us to close the bootstrap argument without controlling the global second spatial momentof the free profile, thereby avoiding the substantial time-dependent losses arising from direct second-moment estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34237",
  "author_total": 1,
  "authors": [
    {
      "name": "Xuan Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5n4qab4shx6w2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34237",
  "fulltext_url": null,
  "id": "5n4qab4shx6w2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34237",
  "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": "W7223814589",
  "pdf_url": "https://arxiv.org/pdf/2610.34237",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5n4qab4shx6w2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34237",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34237"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Almost global existence for quadratic Schrödinger equations in two dimensions",
  "title_text": "Almost global existence for quadratic Schrödinger equations in two dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/5n4qab4shx6w2",
  "venue": "arXiv",
  "versions": []
}