{
  "abstract": "Dispersive and Strichartz estimates are fundamental tools for establishing the well-posedness and long-time behavior of solutions to nonlinear partial differential equations. While these estimates are well-understood in the boundaryless Euclidean setting, the presence of a geometric boundary introduces severe analytical complexities, such as the continuous formation of caustics. In this work, we establish sharp local-in-time dispersive estimates for the semiclassical Schrödinger equation inside a three-dimensional cylindrical domain $Ω\\subset \\mathbb{R}^3$ subject to homogeneous Dirichlet boundary conditions. This paper provides the first comprehensive microlocal treatment for this anisotropic geometric setting, extending the optimal strictly convex boundary results of Ivanovici \\cite{Ivanovici2023} to the parabolic setting. The primary analytical challenge in our cylindrical model stems from the fact that the boundary curvature is non-uniform, depending explicitly on the tracking angle of classical trajectories and vanishing identically along the flat longitudinal axis. Crucially, we demonstrate that the quadratic structure of the Schrödinger phase function ($\\partial_ζ^2 Φ= 2t$) establishes global non-degeneracy, completely bypassing the arduous low-frequency trajectory ray-tracing mandatory in hyperbolic wave equations. By exploiting this structural advantage alongside a streamlined Littlewood-Paley dyadic block decomposition, we prove that the zero-frequency axial tail can be consistently integrated down to the flat limit $η=0$. This yields sharp global Strichartz estimates featuring an explicit derivative loss exponent of $ρ(q) = \\frac{3}{2}\\left(\\frac{1}{2}-\\frac{1}{q}\\right)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13697",
  "author_total": 1,
  "authors": [
    {
      "name": "Len Meas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ksfk254q6vce.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13697",
  "fulltext_url": null,
  "id": "4ksfk254q6vce",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13697",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7213324727",
  "pdf_url": "https://arxiv.org/pdf/2609.13697",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ksfk254q6vce.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13697",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13697"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dispersive and Strichartz Estimates for the Schrödinger Equation Inside Cylindrical Domains",
  "title_text": "Dispersive and Strichartz Estimates for the Schrödinger Equation Inside Cylindrical Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4ksfk254q6vce",
  "venue": "arXiv",
  "versions": []
}