{
  "annotation_id": "042b1c0f-c03a-4433-ab4a-b9781d442f9f",
  "date_created": "2026-03-02T18:01:11.209000Z",
  "date_modified": "2026-03-02T18:01:11.209000Z",
  "file_hash": "b391a87bb545a7276f362500795181960f72de91ec85e6d0c2cfcc1cf4925583",
  "private": false,
  "record": {
    "abstract": "In this paper we continue the analytical study of the sabra shell model of\nenergy turbulent cascade initiated in \\cite{CLT05}. We prove the global\nexistence of weak solutions of the inviscid sabra shell model, and show that\nthese solutions are unique for some short interval of time. In addition, we\nprove that the solutions conserve the energy, provided that the components of\nthe solution satisfy $|{u_n}| \\le C k_n^{-1/3} (\\sqrt{n} \\log(n+1))^{-1}$, for\nsome positive absolute constant $C$, which is the analogue of the Onsager\u0027s\nconjecture for the Euler\u0027s equations. Moreover, we give a Beal-Kato-Majda type\ncriterion for the blow-up of solutions of the inviscid sabra shell model and\nshow the global regularity of the solutions in the ``two-dimensional\u0027\u0027\nparameters regime.",
    "arxiv_id": "physics/0607060",
    "authors": [
      "Peter Constantin",
      "Boris Levant",
      "Edriss S. Titi"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "doi": "10.1103/PhysRevE.75.016304",
    "title": "A Note on the Regularity of Inviscid Shell Model of Turbulence",
    "url": "https://arxiv.org/abs/physics/0607060"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "162cd163-4266-497c-a168-d47a3ac78b82",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}