{
  "annotation_id": "dd6b4c57-23ef-4174-9b29-30a61b9d60f7",
  "date_created": "2026-03-02T18:00:53.310000Z",
  "date_modified": "2026-03-02T18:00:53.310000Z",
  "file_hash": "09e8d85a638fb7d9163cd71c378a4b60669ace830f660e6ba2d37818d9b4bf7b",
  "private": false,
  "record": {
    "abstract": "Some important concepts in the nonstandard analysis theory of turbulence are\npresented in this article. The structure of point, on which differential\nequations are defined, is analyzed. The distinction between the uniform point\nand the non-uniform point, as well as between the standard point and the\nnonstandard point, is showed. A new kind of equations, which differ essentially\nfrom those in existent theory, is emphasized. These new equations can hold at\nnon-uniform points. The applicability of the Navier-Stokes equations to\nturbulence is discussed. Some illustrations of the nonstandard analysis theory\nof turbulence are given too.",
    "arxiv_id": "physics/0411251",
    "authors": [
      "Feng Wu"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "doi": "10.1088/0256-307X/22/10/041",
    "title": "Some Important Concepts in Nonstandard Analysis Theory of Turbulence(The   revised)",
    "url": "https://arxiv.org/abs/physics/0411251"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f523123b-c708-42fd-bf53-f8d1438e2441",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}