{
  "abstract": "We study the Cauchy problem in $\\mathbb{R}^{3}$ for the repulsive compressible Navier-Stokes-Riesz system with Riesz exponent $0<s<1$ and viscosity $0<\\varepsilon\\leq1$, where the Riesz interaction $\\nabla(-Δ)^{-s}(ρ-\\barρ)$ is a generalization of the Coulomb interaction for electrons. For small perturbations of a constant equilibrium, with the solenoidal component of the initial velocity of order $\\mathcal{O}(\\varepsilon)$, we prove the global existence and uniqueness of smooth solutions. We derive time-decay estimates in $L^{2}$ norms and $L^{\\infty}$ norms that capture both uniform-in-$\\varepsilon$ dispersive behavior and viscosity-dependent dissipation. We further establish a global-in-time inviscid limit to the irrotational global solution of the compressible Euler-Riesz system whose initial data consist of the same density and the curl-free component of the velocity, with an explicit convergence rate in $W^{k,p}$ norms. The proof combines viscosity-adapted dispersive estimates, normal-form analysis and nonlinear energy estimates with control of both negative and positive Sobolev norms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.05562",
  "author_total": 3,
  "authors": [
    {
      "name": "Agnieszka Świerczewska-Gwiazda"
    },
    {
      "name": "Yuan Xu"
    },
    {
      "name": "Junhao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frgyr538n8gda.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.05562",
  "fulltext_url": null,
  "id": "frgyr538n8gda",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.05562",
  "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"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7167677250",
  "pdf_url": "https://arxiv.org/pdf/2607.05562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frgyr538n8gda.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2607.05562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.05562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L^{2}-L^{\\infty}$ decay estimates and inviscid limits for Global smooth solutions to the compressible Navier-Stokes-Riesz system",
  "title_text": "L^2−L^∞ decay estimates and inviscid limits for Global smooth solutions to the compressible Navier-Stokes-Riesz system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/frgyr538n8gda",
  "venue": "arXiv",
  "versions": []
}