{
  "id": "1912.13074",
  "version": "v1",
  "published": "2019-12-30T20:18:56.000Z",
  "updated": "2019-12-30T20:18:56.000Z",
  "title": "Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed",
  "authors": [
    "Christian Klingenberg",
    "Ondřej Kreml",
    "Václav Mácha",
    "Simon Markfelder"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The question of (non-)uniqueness of one-dimensional self-similar solutions to the Riemann problem for hyperbolic systems of gas dynamics in sets of multi-dimensional admissible weak solutions was addressed in recent years in several papers culminating in [17] with the proof that the Riemann problem for the isentropic Euler system with a power law pressure is ill-posed if the one-dimensional self-similar solution contains a shock. Natural question then arises whether the same holds also for a more involved system of equations, the full Euler system. After the first step in this direction was made in [1], where the ill-posedness was proved in the case of two shocks appearing in the self-similar solution, we prove in this paper that the presence of just one shock in the self-similar solution implies the same outcome, i.e. the existence of infinitely many admissible weak solutions to the multi-dimensional problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-30T20:18:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35Q31",
      "76N10"
    ],
    "keywords": [
      "full euler system",
      "riemann problem",
      "multiple space dimensions",
      "admissible weak solutions",
      "one-dimensional self-similar solution contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}