{"paper":{"title":"Global existence of small data solutions to 3-D semilinear Euler-Poisson-Darboux equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huicheng Yin, QianQian Li","submitted_at":"2026-07-06T01:03:03Z","abstract_excerpt":"There is an interesting open question: for $n$-D ($n\\ge 1$) semilinear Euler-Poisson-Darboux equation $\\partial_t^2u-\\Delta u+\\frac{\\mu}{t}\\partial_tu=|u|^p$, where $t\\ge 1$, $p>1$ and $\\mu>0$, the global small data weak solution $u$ will exist when $p>p_{crit}(n,\\mu)=\\max\\{p_s(n+\\mu), p_f(n)\\}$ with the Strauss exponent $p_{s}(n+\\mu)=\\frac{n+\\mu+1+\\sqrt{(n+\\mu)^2+10(n+\\mu)-7}}{2(n+\\mu-1)}$ and the Fujita exponent $p_f(n)=1+\\frac{2}{n}$. The blowup of weak solution $u$ has been shown when $1<p\\le p_{crit}(n,\\mu)$ meanwhile this open question has been solved for $n=1,2$. In the present paper, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04575","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04575/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}