{
  "abstract": "We investigate the relaxation problem and the diffusion phenomenon for the compressible Euler system with a time-dependent damping coefficient of the form µ (1+t) λ in R d (d ≥ 1). We establish uniform regularity estimates with respect to the relaxation parameter ε and prove the global wellposedness of classical solutions to the Cauchy problem. In addition, we justify the global-in-time strong convergence of the solutions towards those of a general porous medium-type diffusion system, with an explicit rate of convergence, and for ill-prepared initial data. The core of our proof relies on a refined hypocoercivity framework combined with a new time-dependent frequency decomposition, both adapted to handle damping terms with time-dependent coefficients. This enables us to treat the overdamped regime λ ∈ (-∞, 0) and the underdamped regime λ ∈ (0, 1) for any µ > 0, and also the borderline critical case λ = 1 under the improved condition µ > 2ε 2 .",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Timothée Crin-Barat"
    },
    {
      "name": "Xinghong Pan"
    },
    {
      "name": "Ling-Yun Shou"
    },
    {
      "name": "Qimeng Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2nb5vc0eear8.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "d2nb5vc0eear8",
  "issns": [],
  "landing_url": "https://hal.science/hal-05404720v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05404720/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2nb5vc0eear8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:29Z",
      "native_id": "hal-05404720",
      "source": "hal",
      "url": "https://hal.science/hal-05404720v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Compressible Euler equations with time-dependent damping in the critical regularity setting: global well-posedness and strong relaxation limit",
  "title_text": "Compressible Euler equations with time-dependent damping in the critical regularity setting: global well-posedness and strong relaxation limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:29Z",
  "url": "https://research.draconitic.com/paper/d2nb5vc0eear8",
  "venue": "HAL",
  "versions": []
}