{
  "annotation_id": "b1b1ee42-4410-4976-a273-2f84bef723f4",
  "date_created": "2026-02-17T05:53:04.833000Z",
  "date_modified": "2026-02-17T05:53:04.833000Z",
  "file_hash": "30477c3065c0ee493156af28a030c8ed1da916372a643628b8a232fff1ae98e6",
  "private": false,
  "record": {
    "abstract": "For a $C^1_{t,x}$ solution $u$ to the incompressible 3D Euler equations, the helicity $H(u(t))=\\int_{\\mathbb{T}^3} u \\cdot \\textrm{curl}\\, u$ is constant in time. For general low-regularity weak solutions, it is not always clear how to define the helicity, or whether it must be constant in time in the case that there is a clear definition. In this paper, we define a generalized helicity which extends the classical definitions and construct weak solutions of Euler of almost Onsager-critical regularity in $L^3$ with prescribed generalized helicity and kinetic energy.",
    "arxiv_id": "2601.05869",
    "authors": [
      "Vikram Giri",
      "Hyunju Kwon",
      "Matthew Novack"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Non-conservation of a generalized helicity in the Euler equations",
    "url": "https://arxiv.org/abs/2601.05869",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "84f014fe-7bc9-42b4-a383-65e0986902c3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}