{
  "abstract": "In this study, we analyze the rapid stabilization of Stokes and the two-and threedimensional Navier-Stokes systems in the presence of an unknown spatially localized disturbance. A multivalued feedback control strategy is proposed which combines the Lyapunov frequency method with the multivalued sign operator. This methodology connects Lyapunov-based stability analysis with spectral inequalities, while the inclusion of the sign operator provides robustness against disturbance. The closed-loop system is governed by a differential inclusion, for which well-posedness is proved via the theory of maximal monotone operators. This approach guarantees global rapid exponential stabilization for the Stokes system and local rapid exponential stabilization for the twoand three-dimensional Navier-Stokes systems, with arbitrarily large disturbance bounds. In three dimensions, we obtain global strong solutions and rapid exponential stabilization for initial data sufficiently small in the L 2 -norm with a prescribed, arbitrarily large bound in the H 1 -norm.\n\nL 2 (Ω) n ,",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31790",
  "author_total": 4,
  "authors": [
    {
      "name": "Christian Calle"
    },
    {
      "name": "Patricio Guzmán"
    },
    {
      "name": "Hugo Parada"
    },
    {
      "name": "Jefferson Prada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wb1g0va58100.bib",
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  "doi": "10.48550/arxiv.2610.31790",
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  "id": "1wb1g0va58100",
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  "language": "en",
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  "pdf_url": "https://hal.science/hal-05839066/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
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  "ris": "https://research.draconitic.com/paper/1wb1g0va58100.ris",
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      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05839066",
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      "url": "https://hal.science/hal-05839066v1"
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      "native_id": "2610.31790",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31790"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Rapid stabilization for Stokes and Navier-Stokes systems with localized disturbance",
  "title_text": "Rapid stabilization for Stokes and Navier-Stokes systems with localized disturbance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/1wb1g0va58100",
  "venue": "HAL",
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