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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.08059","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-25T19:49:48Z","cross_cats_sorted":[],"title_canon_sha256":"d9ce32335cfd7cd406b737a9f2ce123893e4141dd7ad1bf6e6d73d713bb0a695","abstract_canon_sha256":"d7aacdc70189fceff64c008432680a36df6b5c1b41c12984e5325d1e2381bc1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:09.546872Z","signature_b64":"cJ7gL2QmCzjVGtOqky+7+Ax41Tn9Y9vbyks+vUB6XTdO2HFD3O9rkDndEOAUI8aiSM+SxZLhu8oqhkpnRNAWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"445372e7d46f0614804da0f04ef3bd50d088bed01382fc17d82c9f5a55f71d30","last_reissued_at":"2026-05-18T00:52:09.546355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:09.546355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $F(v) = \\frac{1}{p+1} |v|^{p+1}$. 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