{
  "id": "2407.05971",
  "version": "v1",
  "published": "2024-07-08T14:11:13.000Z",
  "updated": "2024-07-08T14:11:13.000Z",
  "title": "One-dimensional Carrollian fluids II: $C^1$ blow-up criteria",
  "authors": [
    "Nikolaos Athanasiou",
    "P. Marios Petropoulos",
    "Simon Schulz",
    "Grigalius Taujanskas"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP",
    "gr-qc",
    "hep-th"
  ],
  "abstract": "The Carrollian fluid equations arise from the equations for relativistic fluids in the limit as the speed of light vanishes, and have recently experienced a surge of interest in the theoretical physics community in the context of asymptotic symmetries and flat-space holography. In this paper we initiate the rigorous systematic analysis of these equations by studying them in one space dimension in the $C^1$ setting. We begin by proposing a notion of isentropic Carrollian equations, and use this to reduce the Carrollian equations to a $2 \\times 2$ system of conservation laws. Using the scheme of Lax, we then classify when $C^1$ solutions to the isentropic Carrollian equations exist globally, or blow up in finite time. Our analysis assumes a Carrollian analogue of a constitutive relation for the Carrollian energy density, with exponent in the range $\\gamma \\in (1,3]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-08T14:11:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35L40",
      "35Q35",
      "35Q75",
      "85A30"
    ],
    "keywords": [
      "one-dimensional carrollian fluids",
      "blow-up criteria",
      "isentropic carrollian equations",
      "carrollian fluid equations arise",
      "carrollian energy density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}