{
  "id": "2010.14905",
  "version": "v1",
  "published": "2020-10-28T11:56:12.000Z",
  "updated": "2020-10-28T11:56:12.000Z",
  "title": "Localization of the formation of singularities in multidimensional compressible Euler equations",
  "authors": [
    "Olga Rozanova"
  ],
  "comment": "21 pages, 2 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial stationary state. We prove the blowup results using the characteristics of the propagation of the solution in space and find upper and lower bounds for the density of a smooth solution in a given region of space in terms of the initial data. To solve the problems, we introduce a special family of integral functionals and study their temporal dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-28T11:56:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76N10",
      "35L60",
      "35L67"
    ],
    "keywords": [
      "multidimensional compressible euler equations",
      "singularities",
      "localization",
      "nontrivial stationary state",
      "smooth data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}