{"paper":{"title":"Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2016-06-27T20:47:14Z","abstract_excerpt":"In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as \\begin{align*} \\partial_t \\omega + {\\mathcal L}_u \\omega &= 0\\\\ u &= \\delta \\tilde \\eta^{-1} \\Delta^{-1} \\omega \\end{align*} where $\\omega$ is the vorticity $2$-form, ${\\mathcal L}_u$ denotes the Lie derivative with respect to the velocity field $u$, $\\Delta$ is the Hodge Laplacian, $\\delta$ is the codifferential (the negative of the divergence operator), and $\\tilde \\eta^{-1}$ is the canonical map from $2$-forms to $2$-vector fields induced by the Euclidea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08481","kind":"arxiv","version":2},"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"}