{"paper":{"title":"Global well-posedness for nonlinear wave equations with supercritical source and damping terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yanqiu Guo","submitted_at":"2018-10-30T01:32:36Z","abstract_excerpt":"We prove the global well-posedness of weak solutions for nonlinear wave equations with supercritical source and damping terms on a three-dimensional torus $\\mathbb T^3$ of the prototype \\begin{align*} &u_{tt}-\\Delta u+|u_t|^{m-1}u_t=|u|^{p-1}u, \\;\\; (x,t) \\in \\mathbb T^3 \\times \\mathbb R^+ ; \\notag\\\\ &u(0)=u_0 \\in H^1(\\mathbb T^3)\\cap L^{m+1}(\\mathbb T^3), \\;\\; u_t(0)=u_1\\in L^2(\\mathbb T^3), \\end{align*} where $1\\leq p\\leq \\min\\{ \\frac{2}{3} m + \\frac{5}{3} , m \\}$. Notably, $p$ is allowed to be larger than $6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12476","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":""},"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"}