{
  "id": "1307.4504",
  "version": "v2",
  "published": "2013-07-17T05:05:27.000Z",
  "updated": "2014-11-12T03:34:45.000Z",
  "title": "Global estimates and blow-up criteria for the generalized Hunter-Saxton system",
  "authors": [
    "Alejandro Sarria"
  ],
  "comment": "33 pages, 12 figures, minor modifications, mostly stylistic ones",
  "categories": [
    "math.AP"
  ],
  "abstract": "The generalized, two-component Hunter-Saxton system comprises several well-known models of fluid dynamics and serves as a tool for the study of one-dimensional fluid convection and stretching. In this article a general representation formula for periodic solutions to the system, which is valid for arbitrary values of parameters $(\\lambda,\\kappa)\\in\\mathbb{R}\\times\\mathbb{R}$, is derived. This allows us to examine in great detail qualitative properties of blow-up as well as the asymptotic behaviour of solutions, including convergence to steady states in finite or infinite time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-17T05:05:27.000Z",
      "abstract": "The generalized, two-component Hunter-Saxton system comprises several well-known models of fluid dynamics and serves as a tool for the study of one-dimensional fluid convection and stretching. In this article a general representation formula for periodic solutions to the system, which is valid for arbitrary values of parameters $(\\lambda,\\kappa)\\in\\mathbb{R}\\times\\mathbb{R}$, is derived. This allows us to examine in great detail qualitative properties of blow-up as well as the asymptotic behaviour, including convergence to steady states in finite or infinite time, of solutions.",
      "comment": "33 pages, 12 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-12T03:34:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35B10",
      "35B65",
      "35Q35",
      "35B40"
    ],
    "keywords": [
      "generalized hunter-saxton system",
      "global estimates",
      "blow-up criteria",
      "two-component hunter-saxton system comprises",
      "general representation formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1243263,
      "adsabs": "2013arXiv1307.4504S"
    }
  }
}