{"paper":{"title":"Generalized stochastic Lagrangian paths for the Navier-Stokes equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ana Bela Cruzeiro, Marc Arnaudon (IMB), Shizan Fang (IMB)","submitted_at":"2015-09-11T13:10:44Z","abstract_excerpt":"In the note added in proof of the seminal paper [Groups of diffeomorphisms andthe motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163], Ebinand Marsden introduced the so-called correct Laplacian for the Navier-Stokes equationon a compact Riemannian manifold. In the spirit of Brenier's generalized flows forthe Euler equation, we introduce a class of semimartingales on a compact Riemannianmanifold. We prove that these semimartingales are critical points to the correspondingkinetic energy if and only if its drift term solves weakly the Navier-Stokes equationdefined with Ebin-Marsd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03491","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"}