{
  "id": "1911.04315",
  "version": "v1",
  "published": "2019-11-11T15:03:21.000Z",
  "updated": "2019-11-11T15:03:21.000Z",
  "title": "Incompressible limit of the Ericksen-Leslie hyperbolic liquid crystal model in compressible flow",
  "authors": [
    "Liang Guo",
    "Ning Jiang",
    "Fucai Li",
    "Yi-Long Luo",
    "Shaojun Tang"
  ],
  "comment": "49 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We justify the incompressible limit of the Ericksen-Leslie hyperbolic liquid crystal model in compressible flow in the framework of classical solutions. We first derive the uniform energy estimates on the Mach number $\\eps$ for both the compressible system and its differential system with respect to time under uniformly in $\\eps$ small initial data. Then, based on these uniform estimates, we pass to the limit $\\eps \\rightarrow 0$ in the compressible system, so that we establish the global classical solution of the incompressible system by the compactness arguments. Moreover, we also obtain the convergence rates associated with $L^2$-norm in the case of well-prepared initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-11T15:03:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76A15",
      "35A01",
      "35B40"
    ],
    "keywords": [
      "ericksen-leslie hyperbolic liquid crystal model",
      "compressible flow",
      "incompressible limit",
      "initial data",
      "compressible system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}