{"paper":{"title":"On the quest for generalized Hamiltonian descriptions of $3D$-flows generated by curl of a vector potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"O\\u{g}ul Esen, Partha Guha","submitted_at":"2019-06-11T10:08:03Z","abstract_excerpt":"We study Hamiltonian analysis of three-dimensional advection flow $\\mathbf{\\dot{x}}=\\mathbf{v}({\\bf x})$ of incompressible nature $\\nabla \\cdot {\\bf v} ={\\bf 0}$ assuming that dynamics is generated by the curl of a vector potential $\\mathbf{v} = \\nabla \\times \\mathbf{A}$. More concretely, we elaborate Nambu-Hamiltonian and bi-Hamiltonian characters of such systems under the light of vanishing or non-vanishing of the quantity $\\mathbf{A} \\cdot \\nabla \\times \\mathbf{A}$. We present an example (satisfying $\\mathbf{A} \\cdot \\nabla \\times \\mathbf{A} \\neq 0$) which can be written as in the form of N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04476","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.04476/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}