{
  "id": "2407.05972",
  "version": "v1",
  "published": "2024-07-08T14:13:04.000Z",
  "updated": "2024-07-08T14:13:04.000Z",
  "title": "One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^\\infty$",
  "authors": [
    "P. Marios Petropoulos",
    "Simon Schulz",
    "Grigalius Taujanskas"
  ],
  "comment": "31 pages",
  "categories": [
    "math.AP",
    "gr-qc",
    "hep-th"
  ],
  "abstract": "The Carrollian fluid equations arise as the $c \\to 0$ limit of the relativistic fluid equations and have recently experienced a surge of activity in the flat-space holography community. However, the rigorous mathematical well-posedness theory for these equations does not appear to have been previously studied. This paper is the third in a series in which we initiate the systematic analysis of the Carrollian fluid equations. In the present work we prove the global-in-time existence of bounded entropy solutions to the isentropic Carrollian fluid equations in one spatial dimension for a particular constitutive law ($\\gamma = 3$). Our method is to use a vanishing viscosity approximation for which we establish a compensated compactness framework. Using this framework we also prove the compactness of entropy solutions in $L^\\infty$, and establish a kinetic formulation of the problem. This global existence result in $L^\\infty$ extends the $C^1$ theory presented in our companion paper ``One-Dimensional Carrollian Fluids II: $C^1$ Blow-up Criteria''.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-08T14:13:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35Q35",
      "35Q75",
      "85A30"
    ],
    "keywords": [
      "one-dimensional carrollian fluids",
      "weak continuity",
      "carrollian fluid equations arise",
      "entropy solutions",
      "isentropic carrollian fluid equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}