{
  "annotation_id": "00490090-d2b7-46d5-978c-fddd0a8bd3f3",
  "date_created": "2026-03-02T18:00:38.770000Z",
  "date_modified": "2026-03-02T18:00:38.770000Z",
  "file_hash": "5374bc6d4a96830bf575a71c1f72827f86676fb6ce104baf3c64b2a8a9c3e521",
  "private": false,
  "record": {
    "abstract": "A sufficient integral criterion for a blow-up solution of the Hopf equations\n(the Euler equations with zero pressure) is found. This criterion shows that a\ncertain positive integral quantity blows up in a finite time under specific\ninitial conditions. Blow-up of this quantity means that solution of the Hopf\nequation in 3D can not be continued in the Sobolev space $H^2({\\cal R}^3)$ for\ninfinite time.",
    "arxiv_id": "physics/0204080",
    "authors": [
      "E. A. Kuznetsov"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "doi": "10.1016/S0167-2789(03)00225-2",
    "title": "Towards a sufficient criterion for collapse in 3D Euler equations",
    "url": "https://arxiv.org/abs/physics/0204080"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7123b646-ba45-4079-bcc6-82fc88c86960",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}