{"paper":{"title":"On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2019-02-17T19:52:33Z","abstract_excerpt":"The incompressible Euler equations on a compact Riemannian manifold $(M,g)$ take the form \\begin{align*} \\partial_t u + \\nabla_u u &= - \\mathrm{grad}_g p \\\\ \\mathrm{div}_g u &= 0, \\end{align*} where $u: [0,T] \\to \\Gamma(T M)$ is the velocity field and $p: [0,T] \\to C^\\infty(M)$ is the pressure field. In this paper we show that if one is permitted to extend the base manifold $M$ by taking an arbitrary warped product with a torus, then the space of solutions to this equation becomes \"non-rigid'\"in the sense that a non-empty open set of smooth incompressible flows $u: [0,T] \\to \\Gamma(T M)$ can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06313","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"}