{"paper":{"title":"Finite time blowup for high dimensional nonlinear wave systems with bounded smooth nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2016-03-07T01:24:37Z","abstract_excerpt":"We consider the global regularity problem for nonlinear wave systems $$ \\Box u = f(u) $$ on Minkowski spacetime ${\\bf R}^{1+d}$ with d'Alambertian $\\Box := -\\partial_t^2 + \\sum_{i=1}^d \\partial_{x_i}^2$, where the field $u \\colon {\\bf R}^{1+d} \\to {\\bf R}^m$ is vector-valued, and the nonlinearity $f \\colon {\\bf R}^m \\to {\\bf R}^m$ is a smooth function with $f(0)=0$ and all derivatives bounded; the higher-dimensional sine-Gordon equation $\\Box u = \\sin u$ is a model example of this class of nonlinear wave system. For dimensions $d \\leq 9$, it follows from the work of Heinz, Pecher, Brenner, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01908","kind":"arxiv","version":3},"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"}