{
  "id": "2403.16642",
  "version": "v2",
  "published": "2024-03-25T11:29:02.000Z",
  "updated": "2024-04-07T13:35:45.000Z",
  "title": "Self-dual solution of 3D incompressible Navier-Stokes equations",
  "authors": [
    "Ning-An Lai",
    "Yi Zhou"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Whether the 3D incompressible Navier-Stokes equations will have a global smooth solution for all smooth, finite energy initial data is a Millennium Prize problem. One of the main difficulties of this problem is that the Navier-Stokes equations are actually a system of semilinear heat equations rather than a single equation. In this paper, we discover a remarkable hidden symmetry of the 3D incompressible Navier-Stokes equations. Under this symmetric reduction, the system reduces to a single scalar semilinear heat equation. The symmetry also holds for the 3D incompressible Euler equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-04-07T13:35:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d incompressible navier-stokes equations",
      "self-dual solution",
      "single scalar semilinear heat equation",
      "finite energy initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}