{
  "id": "math/0507254",
  "version": "v1",
  "published": "2005-07-13T15:16:38.000Z",
  "updated": "2005-07-13T15:16:38.000Z",
  "title": "On the True Nature of Turbulence",
  "authors": [
    "Y. Charles Li"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "nlin.CD",
    "physics.flu-dyn"
  ],
  "abstract": "In this article, I would like to express some of my views on the nature of turbulence. These views are mainly drawn from the author's recent results on chaos in partial differential equations \\cite{Li04}. Fluid dynamicists believe that Navier-Stokes equations accurately describe turbulence. A mathematical proof on the global regularity of the solutions to the Navier-Stokes equations is a very challenging problem. Such a proof or disproof does not solve the problem of turbulence. It may help understanding turbulence. Turbulence is more of a dynamical system problem. Studies on chaos in partial differential equations indicate that turbulence can have Bernoulli shift dynamics which results in the wandering of a turbulent solution in a fat domain in the phase space. Thus, turbulence can not be averaged. The hope is that turbulence can be controlled.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-13T15:16:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76-02",
      "37-02",
      "35-02"
    ],
    "keywords": [
      "turbulence",
      "true nature",
      "partial differential equations",
      "navier-stokes equations",
      "bernoulli shift dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7254L"
    }
  }
}