{"paper":{"title":"Finite time blowup for a supercritical defocusing nonlinear Schr\\\"odinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2016-12-02T00:41:50Z","abstract_excerpt":"We consider the global regularity problem for defocusing nonlinear Schr\\\"odinger systems $$ i \\partial_t + \\Delta u = (\\nabla_{{\\bf R}^m} F)(u) + G $$ on Galilean spacetime ${\\bf R} \\times {\\bf R}^d$, where the field $u\\colon {\\bf R}^{1+d} \\to {\\bf C}^m$ is vector-valued, $F\\colon {\\bf C}^m \\to {\\bf R}$ is a smooth potential which is positive, phase-rotation-invariant, and homogeneous of order $p+1$ outside of the unit ball for some exponent $p >1$, and $G: {\\bf R} \\times {\\bf R}^d \\to {\\bf C}^m$ is a smooth, compactly supported forcing term. This generalises the scalar defocusing nonlinear Sc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00526","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"}