{
  "abstract": "We investigate the maximization problem for the family of mixed-norm Strichartz inequalities for the Schrödinger equation, $\\|e^{-itΔ/2}f\\|_{L_t^qL_{\\boldsymbol{x}}^r(\\mathbb{R}^{1+d})}\\le C_{q,r}\\lVert f\\rVert_{L^2(\\mathbb{R}^d)}$, with $2/q+d/r=d/2$, $q,r\\geq 2$, and thus $r\\leq 2d/(d-2)$ if $d\\geq 3$. We show that, in low dimensions $1\\leq d\\leq 5$, the thresholds $ρ_1=10$, $ρ_2=6$, $ρ_3=4\\sqrt{7}-6\\approx 4.583$, $ρ_4=2\\sqrt{15}-4\\approx 3.746$, and $ρ_5=10/3\\approx 3.333$ are such that gaussians are stable local maximizers for $2<r<ρ_d$, and fail to be local maximizers for $ρ_d<r\\leq 2d/(d-2)$ (with the conventions there is no upper bound on $r$ when $d\\in\\{1,2\\}$ and that $r=\\infty$ is excluded when $d=2$). In the cases $(q,r,d)\\in\\{(6,6,1),(8,4,1),(4,4,2)\\}$, we establish global stability inequalities with effective stability constants. Both proofs hinge on spectral gaps which we compute exactly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11644",
  "author_total": 3,
  "authors": [
    {
      "name": "Felipe Gonçalves"
    },
    {
      "name": "Giuseppe Negro"
    },
    {
      "name": "Diogo Oliveira e Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/566fg9gnrnq8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11644",
  "fulltext_url": null,
  "id": "566fg9gnrnq8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11644",
  "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"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212285607",
  "pdf_url": "https://arxiv.org/pdf/2609.11644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/566fg9gnrnq8m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11644"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gaussians Do Not Always Maximize Mixed-Norm Strichartz Inequalities for the Schrödinger Equation",
  "title_text": "Gaussians Do Not Always Maximize Mixed-Norm Strichartz Inequalities for the Schrödinger Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/566fg9gnrnq8m",
  "venue": "arXiv",
  "versions": []
}