{"paper":{"title":"Finite time blowup for an averaged three-dimensional Navier-Stokes equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2014-02-03T06:18:56Z","abstract_excerpt":"The Navier-Stokes equation on the Euclidean space $\\mathbf{R}^3$ can be expressed in the form $\\partial_t u = \\Delta u + B(u,u)$, where $B$ is a certain bilinear operator on divergence-free vector fields $u$ obeying the cancellation property $\\langle B(u,u), u\\rangle=0$ (which is equivalent to the energy identity for the Navier-Stokes equation). In this paper, we consider a modification $\\partial_t u = \\Delta u + \\tilde B(u,u)$ of this equation, where $\\tilde B$ is an averaged version of the bilinear operator $B$ (where the average involves rotations and Fourier multipliers of order zero), and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0290","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"}