{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GMNPU3FCQPHVOXU3BXKCQANDHN","short_pith_number":"pith:GMNPU3FC","schema_version":"1.0","canonical_sha256":"331afa6ca283cf575e9b0dd42801a33b7399ff9866a2381f57885621ec13ac1b","source":{"kind":"arxiv","id":"2607.04575","version":1},"attestation_state":"computed","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 $11$ 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