{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PK4ONXILYDDPDCYSXS2MZKPO2U","short_pith_number":"pith:PK4ONXIL","schema_version":"1.0","canonical_sha256":"7ab8e6dd0bc0c6f18b12bcb4cca9eed5264af58cc27de1dc0aab140435a85fe4","source":{"kind":"arxiv","id":"2503.18677","version":2},"attestation_state":"computed","paper":{"title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, I","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Qianqian, Wang Dinghuai, Yin Huicheng","submitted_at":"2025-03-24T13:49:29Z","abstract_excerpt":"There is an interesting open question: for the $n$-D ($n\\ge 1$) semilinear wave equation with scale-invariant damping $\\partial_t^2u-\\Delta u+\\frac{\\mu}{t}\\partial_tu=|u|^p$, 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 $p_{s}(n+\\mu)=\\frac{n+\\mu+1+\\sqrt{(n+\\mu)^2+10(n+\\mu)-7}}{2(n+\\mu-1)}$ and $p_f(n)=1+\\frac{2}{n}$. It is noticed that the weak solution $u$ can blow up in finite time 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 $p_{s}(n+\\mu)=\\frac{n+\\mu+1+\\sqrt{(n+\\mu)^2+10(n+\\mu)-7}}{2(n+\\mu-1)}$ and $p_f(n)=1+\\frac{2}{n}$. It is noticed that the weak solution $u$ can blow up in finite time when $1