{
  "annotation_id": "e68be857-024a-4da3-b354-38b44c204634",
  "date_created": "2026-03-02T18:01:11.222000Z",
  "date_modified": "2026-03-02T18:01:11.222000Z",
  "file_hash": "e779120a0a670f64fe74284985107df6169f108ff3d088b443da7352b42bd9a0",
  "private": false,
  "record": {
    "abstract": "In this paper, we perform a careful numerical study of nearly singular\nsolutions of the 3D incompressible Euler equations with smooth initial data. We\nconsider the interaction of two perturbed antiparallel vortex tubes which was\npreviously investigated by Kerr in \\cite{Kerr93,Kerr05}. In our numerical\nstudy, we use both the pseudo-spectral method with the 2/3 dealiasing rule and\nthe pseudo-spectral method with a high order Fourier smoothing. Moreover, we\nperform a careful resolution study with grid points as large as\n$1536\\times1024\\times 3072$ to demonstrate the convergence of both numerical\nmethods. Our computational results show that the maximum vorticity does not\ngrow faster than doubly exponential in time while the velocity field remains\nbounded up to T=19, beyond the singularity time $T=18.7$ reported by Kerr in\n\\cite{Kerr93,Kerr05}. The local geometric regularity of vortex lines near the\nregion of maximum vorticity seems to play an important role in depleting the\nnonlinear vortex stretching dynamically.",
    "arxiv_id": "physics/0608126",
    "authors": [
      "Thomas Y. Hou",
      "Ruo Li"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "title": "Numerical Study of Nearly Singular Solutions of the 3-D Incompressible   Euler Equations",
    "url": "https://arxiv.org/abs/physics/0608126"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "247e9e53-4e76-4477-93c7-b5b548f477ab",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}