{
  "annotation_id": "c5f72c3b-55c9-4bd5-a1ef-8c88017404d1",
  "date_created": "2026-03-02T18:00:53.633000Z",
  "date_modified": "2026-03-02T18:00:53.633000Z",
  "file_hash": "a73bfe9d1481fcc5e34f7e53529fdefe861e0a18b8e01bea07f870323576cad8",
  "private": false,
  "record": {
    "abstract": "It can be observed that the differential operators of fluid mechanics can be\ndefined in terms of the complete derivative on the finite - dimensional affine\nspace. It follows from the fact that all norms on the finite - dimensional\nvector space are equivalent and from the definition of the complete derivative\non the normed affine spaces (see: L.Schwartz, Analyse Mathematique, Hermann,\n1967). In particular, it is shown that the \"substantial derivative\" of the\nstandard formulation is a directional derivative along the \"non - relativistic\nfour - velocity\".",
    "arxiv_id": "physics/0411154",
    "authors": [
      "S. Piekarski"
    ],
    "categories": [
      "physics.flu-dyn",
      "physics.gen-ph"
    ],
    "title": "On the invariant formulation of fluid mechanics",
    "url": "https://arxiv.org/abs/physics/0411154"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ea8b5667-954e-4973-b969-5920fb6ca36b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}