{
  "id": "1506.04561",
  "version": "v1",
  "published": "2015-06-15T11:55:24.000Z",
  "updated": "2015-06-15T11:55:24.000Z",
  "title": "The Euler and Navier-Stokes equations revisited",
  "authors": [
    "Peter Stubbe"
  ],
  "comment": "13 pages, no figures",
  "categories": [
    "physics.flu-dyn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The present paper is motivated by recent mathematical work on the incompressible Euler and Navier-Stokes equations, partly having physically problematic results and unrealistic expectations. The Euler and Navier-Stokes equations are rederived here from the roots, starting at the kinetic equation for the distribution function in phase space. The derivation shows that the Euler and Navier-Stokes equations are valid only if the fluid under consideration is an ideal gas, and if deviations from equilibrium are small in a defined sense, thereby excluding fully nonlinear solutions. Furthermore, the derivation shows that the Euler and Navier-Stokes equations are unseparably coupled with an appertaining equation for the temperature, whereby, in conjunction with the continuity equation, a closed system of transport equations is set up which leaves no room for any additional equation, with the consequence that the frequently used incompressibility condition $\\nabla\\cdot{\\bf v}=0$ can, at best, be applied to simplify these transport equations, but not to supersede any of them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-15T11:55:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "navier-stokes equations",
      "transport equations",
      "kinetic equation",
      "incompressibility condition",
      "distribution function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}