{
  "id": "2103.04905",
  "version": "v1",
  "published": "2021-03-08T17:09:44.000Z",
  "updated": "2021-03-08T17:09:44.000Z",
  "title": "Global ill-posedness for a dense set of initial data to the Isentropic system of gas dynamics",
  "authors": [
    "Robin Ming Chen",
    "Alexis F. Vasseur",
    "Cheng Yu"
  ],
  "comment": "1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In dimension $n=2$ and $3$, we show that for any initial datum belonging to a dense subset of the energy space, there exist infinitely many global-in-time admissible weak solutions to the isentropic Euler system whenever $1<\\gamma\\leq 1+\\frac2n$. This result can be regarded as a compressible counterpart of the one obtained by Szekelyhidi--Wiedemann (ARMA, 2012) for incompressible flows. Similarly to the incompressible result, the admissibility condition is defined in its integral form. Our result is based on a generalization of a key step of the convex integration procedure. This generalization allows, even in the compressible case, to convex integrate any smooth positive Reynolds stress. A large family of subsolutions can then be considered. These subsolutions can be generated, for instance, via regularization of any weak inviscid limit of an associated compressible Navier--Stokes system with degenerate viscosities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-08T17:09:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "76N10",
      "35L65"
    ],
    "keywords": [
      "initial datum",
      "global ill-posedness",
      "gas dynamics",
      "isentropic system",
      "dense set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}