{
  "annotation_id": "498b1426-2c48-4c5d-8908-37078d2c8871",
  "date_created": "2026-03-02T18:02:51.350000Z",
  "date_modified": "2026-03-02T18:02:51.350000Z",
  "file_hash": "159c245013c01145aa106e99d594c419780466d17fa06c119cc32ded3e487bfb",
  "private": false,
  "record": {
    "abstract": "Three dimensional unsteady flow of fluids in the Lagrangian description is\nconsidered as an autonomous dynamical system in four dimensions. The condition\nfor the existence of a symplectic structure on the extended space is the frozen\nfield equations of the Eulerian description of motion. Integral invariants of\nsymplectic flow are related to conservation laws of the dynamical equation. A\nscheme generating infinite families of symmetries and invariants is presented.\nFor the Euler equations these invariants are shown to have a geometric origin\nin the description of flow as geodesic motion; they are also interpreted in\nconnection with the particle relabelling symmetry.",
    "arxiv_id": "solv-int/9703012",
    "authors": [
      "H. Gumral"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1016/S0375-9601(97)00404-0",
    "title": "Lagrangian Description, Symplectic Structure, and Invariants of 3D Fluid   Flow",
    "url": "https://arxiv.org/abs/solv-int/9703012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1d4782bb-aeb2-418c-b8d5-c2add8097026",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}