{
  "abstract": "We study critical Strichartz estimates for the resonant hyperbolic Schrödinger flow on the waveguide $\\mathbb{R} \\times \\mathbb{T}^2$. For initial data localized to frequencies at most $N$, we prove that the unit-time $L^2\\to L^{10/3}$ operator norm has sharp order $N^{1/5}$. We further track its dependence on the observation length, obtaining sharp estimates in the short- and long-time regimes and characterizing the frequency-dependent intervals on which the critical estimate remains lossless. The precise dependence on $T$ in the intermediate regime $N^{-1}<T<1$ remains open. The upper bounds are obtained by lifting the global endpoint estimate on the elliptic cylinder $\\mathbb{R} \\times \\mathbb{T}$ to Hilbert-valued data, preserving its time summability, and combining this with periodic Bernstein and interpolation. The lower bounds exploit an exact integer null direction in the periodic frequency lattice together with a suitably scaled Euclidean wave packet. Finally, using a Bloch--Floquet transference argument, we recover the known elliptic unit-time estimate from compact torus theory and obtain a lossless elliptic estimate on frequency-dependent short time intervals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30437",
  "author_total": 2,
  "authors": [
    {
      "name": "Xi Cen"
    },
    {
      "name": "Zhezhi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4y588dn785mv2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30437",
  "fulltext_url": null,
  "id": "4y588dn785mv2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30437",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7214584419",
  "pdf_url": "https://arxiv.org/pdf/2609.30437",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4y588dn785mv2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.30437",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30437"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Sharp critical Strichartz estimates for a resonant hyperbolic Schrödinger flow on the 3D waveguide",
  "title_text": "Sharp critical Strichartz estimates for a resonant hyperbolic Schrödinger flow on the 3D waveguide",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/4y588dn785mv2",
  "venue": "arXiv",
  "versions": []
}