{"paper":{"title":"On the global behavior of weak null quasilinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabio Pusateri, Yu Deng","submitted_at":"2018-04-13T20:13:53Z","abstract_excerpt":"We consider a class of quasilinear wave equations in $3+1$ space-time dimensions that satisfy the \"weak null condition\" as defined by Lindblad and Rodnianski \\cite{LR1}, and study the large time behavior of solutions to the Cauchy problem. The prototype for the class of equations considered is $-\\partial_t^2 u + (1+u) \\Delta u = 0$. Global solutions for such equations have been constructed by Lindblad \\cite{Lindblad1,Lindblad2} and Alinhac \\cite{Alinhac1}. Our main results are the derivation of a precise asymptotic system with good error bounds, and a detailed description of the behavior of so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05107","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"}