{
  "id": "2107.10618",
  "version": "v1",
  "published": "2021-07-22T12:36:42.000Z",
  "updated": "2021-07-22T12:36:42.000Z",
  "title": "A General Convex Integration Scheme for the Isentropic Compressible Euler Equations",
  "authors": [
    "Tomasz Dębiec",
    "Jack W. D. Skipper",
    "Emil Wiedemann"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove via convex integration a result that allows to pass from a so-called subsolution of the isentropic Euler equations (in space dimension at least $2$) to exact weak solutions. The method is closely related to the incompressible scheme established by De Lellis--Sz\\'ekelyhidi, in particular we only perturb momenta and not densities. Surprisingly, though, this turns out not to be a restriction, as can be seen from our simple characterization of the $\\Lambda$-convex hull of the constitutive set. An important application of our scheme will be exhibited in forthcoming work by Gallenm\\\"uller--Wiedemann.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-22T12:36:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31"
    ],
    "keywords": [
      "general convex integration scheme",
      "isentropic compressible euler equations",
      "isentropic euler equations",
      "exact weak solutions",
      "space dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}