{
  "abstract": "For the 3D semilinear Euler-Poisson-Darboux equation $\\square u+\\fracμ{t}\\partial_tu=|u|^p$, where $t\\geq1$, $μ>0$ and $p>1$, it is conjectured that there is a critical exponent $p_{crit}(3,μ)=\\max\\{p_s(3+μ), p_f(3)\\}$ with the Strauss exponent $p_s(3+μ)=\\frac{μ+4+\\sqrt{μ^2+16μ+32}}{2(μ+2)}$ and the Fujita exponent $p_f(3)=\\frac{5}{3}$ such that when $p>p_{crit}(3,μ)$, the small data solution $u$ exists globally, otherwise, when $1<p\\le p_{crit}(3,μ)$, the solution $u$ can blow up in finite time. It is pointed out that for $1<p\\le p_{crit}(3,μ)$, the blowup of solution $u$ has been shown. However, it is still open for the global existence of small solution $u$ when $p>p_{crit}(3,μ)$. Note that $p_{crit}(3,μ)=p_s(3+μ)$ for $0<μ<\\frac{14}{5}$ and $p_{crit}(3,μ)=p_f(3)$ for $μ\\geq\\frac{14}{5}$. In the recent paper [16], the authors have obtained the global small solution $u$ for $p>\\max\\{\\frac{5}{3},1+\\frac{2}μ\\}$ and $μ\\geq\\frac{14}{5}$. In this paper, by utilizing the hypergeometric Riemann representation and establishing some delicate pointwise spacetime weighted estimates, we prove the global existence of small data radial solution $u$ in the remaining range of $\\frac{5}{3}<p\\leq1+\\frac{2}μ$ and $\\frac{14}{5}\\leqμ<3$. Therefore, for the radially symmetric case and $μ\\geq\\frac{14}{5}$, the global existence problem of small data solution $u$ is solved when $p>p_{crit}(3,μ)=\\frac{5}{3}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29258",
  "author_total": 3,
  "authors": [
    {
      "name": "Qianqian Li"
    },
    {
      "name": "Qiao Xin"
    },
    {
      "name": "Huicheng Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cfdta8cd89dn0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29258",
  "fulltext_url": null,
  "id": "cfdta8cd89dn0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29258",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7204971282",
  "pdf_url": "https://arxiv.org/pdf/2608.29258",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cfdta8cd89dn0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29258",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29258"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global small data radial symmetric solutions of 3D semilinear Euler-Poisson-Darboux equations",
  "title_text": "Global small data radial symmetric solutions of 3D semilinear Euler-Poisson-Darboux equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/cfdta8cd89dn0",
  "venue": "arXiv",
  "versions": []
}