{
  "id": "1812.00082",
  "version": "v1",
  "published": "2018-11-30T22:47:38.000Z",
  "updated": "2018-11-30T22:47:38.000Z",
  "title": "On a nonlocal differential equation describing roots of polynomials under differentiation",
  "authors": [
    "Rafael Granero-Belinchón"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "In this work we study the nonlocal transport equation derived recently by Steinerberger when studying how the distribution of roots of a polynomial behaves under iterated differentation of the function. In particular, we study the well-posedness of the equation, establish some qualitative properties of the solution and give conditions ensuring the global existence of both weak and strong solutions. Finally, we present a link between the equation obtained by Steinerberger and a one-dimensional model of the surface quasi-geostrophic equation used by Chae, C\\'ordoba, C\\'ordoba and Fontelos.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-30T22:47:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlocal differential equation",
      "differentiation",
      "nonlocal transport equation",
      "surface quasi-geostrophic equation",
      "polynomial behaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}