{
  "id": "2311.18308",
  "version": "v1",
  "published": "2023-11-30T07:25:52.000Z",
  "updated": "2023-11-30T07:25:52.000Z",
  "title": "Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in $\\R^3$",
  "authors": [
    "Yongqian Han"
  ],
  "comment": "8 page",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The incompressible Navier-Stokes equations are considered. We find that there exist infinite non-trivial solutions of static Euler equations. Moreover there exist random solutions of static Euler equations. Provided Reynolds number is large enough and time variable $t$ goes to infinity, these random solutions of static Euler equations are the path limits of corresponding Navier-Stokes flows. But the double limit of these Navier-Stokes flows do not exist. Therefore these solutions are called turbulent solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-30T07:25:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05",
      "76F02",
      "37L20"
    ],
    "keywords": [
      "incompressible navier-stokes equations",
      "turbulent global solutions",
      "static euler equations",
      "symplectic representation",
      "random solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}