{
  "abstract": "Energy-based analysis of the three-dimensional incompressible Navier--Stokes equations with spatially localized dissipation is developed at the level of kinetic energy and Leray--Hopf weak solutions. A localized coercivity property linking viscosity and damping to global $L^2$ control is introduced and related to observability and spectral inequalities for the associated Stokes operator. Under this condition, exponential energy decay is established without regularity or linearization assumptions, and time-dependent damping is treated within a nonautonomous framework. A finite-dimensional spectral quantity is proposed as a computable proxy for coercivity, yielding explicit decay estimates for reduced-order models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03164",
  "author_total": 1,
  "authors": [
    {
      "name": "Amadou Cissé"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ntdq9z13ww55.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03164",
  "fulltext_url": null,
  "id": "1ntdq9z13ww55",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03164",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
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    [
      "arxiv",
      "math.OC"
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    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7208777555",
  "pdf_url": "https://arxiv.org/pdf/2609.03164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ntdq9z13ww55.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03164"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Energy Decay Induced by Localized Coercivity in the 3D Navier--Stokes Equations",
  "title_text": "Energy Decay Induced by Localized Coercivity in the 3D Navier--Stokes Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/1ntdq9z13ww55",
  "venue": "arXiv",
  "versions": []
}