{"paper":{"title":"Helicity is the only invariant of incompressible flows whose derivative is continuous in $C^1$-topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.DS","authors_text":"Elena A. Kudryavtseva","submitted_at":"2015-11-12T01:17:33Z","abstract_excerpt":"Let $Q$ be a smooth compact orientable 3--manifold with smooth boundary $\\partial Q$. Let $\\mathcal{B}$ be the set of exact 2--forms $B\\in\\Omega^2(Q)$ such that $j_{\\partial Q}^*B=0$, where $j_{\\partial Q}:{\\partial Q}\\to Q$ is the inclusion map. The group $\\mathcal{D}=\\mathrm{Diff}_0(Q)$ of self-diffeomorphisms of $Q$ isotopic to the identity acts on the set $\\mathcal{B}$ by $\\mathcal{D}\\times\\mathcal{B}\\to\\mathcal{B}$, $(h,B)\\mapsto h^*B$. Let $\\mathcal{B}^\\circ$ be the set of 2--forms $B\\in\\mathcal{B}$ without zeros. We prove that every $\\mathcal{D}$--invariant functional $I:\\mathcal{B}^\\ci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03746","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"}