{
  "id": "1707.09794",
  "version": "v1",
  "published": "2017-07-31T10:28:21.000Z",
  "updated": "2017-07-31T10:28:21.000Z",
  "title": "A tribute to conservation of energy for weak solutions",
  "authors": [
    "Tomasz Dębiec",
    "Piotr Gwiazda",
    "Agnieszka Świerczewska-Gwiazda"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolution of the famous Onsager conjecture - which states regularity requirements for weak solutions of the incompressible Euler system to conserve energy. Further we survey results providing optimal sufficient regularity conditions for energy conservation for other balance laws: compressible Euler, Navier-Stokes, magnetohydrodynamics and general conservation laws.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-31T10:28:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35B65",
      "35L65"
    ],
    "keywords": [
      "weak solutions",
      "optimal sufficient regularity conditions",
      "energy conservation",
      "general conservation laws",
      "states regularity requirements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}