{"paper":{"title":"Finite time blowup for a supercritical defocusing nonlinear wave system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2016-02-25T19:49:48Z","abstract_excerpt":"We consider the global regularity problem for defocusing nonlinear wave systems $$ \\Box u = (\\nabla_{{\\bf R}^m} F)(u) $$ on Minkowski spacetime ${\\bf R}^{1+d}$ with d'Alambertian $\\Box := -\\partial_t^2 + \\sum_{i=1}^d \\partial_{x_i}^2$, the field $u: {\\bf R}^{1+d} \\to {\\bf R}^m$ is vector-valued, and $F: {\\bf R}^m \\to {\\bf R}$ is a smooth potential which is positive and homogeneous of order $p+1$ outside of the unit ball, for some $p >1$. This generalises the scalar defocusing nonlinear wave (NLW) equation, in which $m=1$ and $F(v) = \\frac{1}{p+1} |v|^{p+1}$. It is well known that in the energy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08059","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"}