{
  "abstract": "On the Euclidean disk, we construct a nontrivial solution of the Schrödinger (resp. wave) equation with Dirichlet boundary conditions which vanishes identically on a smaller concentric disk for all times. The equation has an additional potential term which is a smooth function having Gevrey 2 + ε (resp. 1 + ε) regularity in time. This shows optimality of the local and global results of the authors [FLL25] (resp. of Tataru-Robbiano-Zuily-Hörmander [Tat95, RZ98, Hör97, Tat99]), stating that Gevrey 2 (resp. Gevrey 1) regularity of the potential yields unique continuation. In turn, this proves that Gevrey 2 (resp. Gevrey 1) regularity in time is critical for the approximate controllability of the Schrödinger (resp. wave) equation. Our construction builds on those of Kumano-go [Kg63] and Takase [Tak21].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Spyridon Filippas"
    },
    {
      "name": "Camille Laurent"
    },
    {
      "name": "Matthieu Léautaud"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eajmcm85756a9.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "eajmcm85756a9",
  "issns": [],
  "landing_url": "https://hal.science/hal-05830608v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05830608/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eajmcm85756a9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "hal-05830608",
      "source": "hal",
      "url": "https://hal.science/hal-05830608v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "INVISIBLE SOLUTIONS FOR SCHRÖDINGER AND WAVE EQUATIONS",
  "title_text": "INVISIBLE SOLUTIONS FOR SCHRÖDINGER AND WAVE EQUATIONS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/eajmcm85756a9",
  "venue": "HAL",
  "versions": []
}