{"paper":{"title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huicheng Yin, QianQian Li","submitted_at":"2025-07-11T02:49:07Z","abstract_excerpt":"For the $2$-D semilinear wave equation with scale-invariant damping $\\square u+\\frac{\\mu}{t}\\partial_tu=|u|^p$, where $t\\geq 1$, $\\mu>0$ and $p>1$, it is conjectured that the global small data weak solution $u$ exists when $p>p_{s}(2+\\mu) =\\frac{\\mu+3+\\sqrt{\\mu^2+14\\mu+17}}{2(\\mu+1)}$ for $0<\\mu\\leq 2$ and $p>p_f(2)=2$ for $\\mu\\geq 2$. In our previous papers, the global small solution $u$ has been obtained for $p>p_{s}(2+\\mu)$ and $0<\\mu<2$ but $\\mu\\not=1$. In the present paper, by the vector field method together with the delicate analysis on the Bessel functions, we will show the global exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08274","kind":"arxiv","version":2},"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/2507.08274/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"}