{"paper":{"title":"Stretching and folding processes in the 3D Euler and Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"D. D. Holm, J. D. Gibbon","submitted_at":"2013-11-02T15:36:19Z","abstract_excerpt":"Stretching and folding dynamics in the incompressible, stratified 3D Euler and Navier-Stokes equations are reviewed in the context of the vector $\\bdB = \\nabla q\\times\\nabla\\theta$ where $q=\\bom\\cdot\\nabla\\theta$. The variable $\\theta$ is the temperature and $\\bdB$ satisfies $\\partial_{t}\\bdB = \\mbox{curl}\\,(\\bu\\times\\bdB)$. These ideas are then discussed in the context of the full compressible Navier-Stokes equations where $q$ takes the two forms $q = \\bom\\cdot\\nabla\\rho$ and $q = \\bom\\cdot\\nabla(\\ln\\rho)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0382","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"}