{
  "id": "1609.03231",
  "version": "v1",
  "published": "2016-09-11T23:41:38.000Z",
  "updated": "2016-09-11T23:41:38.000Z",
  "title": "On the $L^p$ regularity of solutions to the generalized Hunter-Saxton system",
  "authors": [
    "Jaeho Choi",
    "Nitin Krishna",
    "Nicole Magill",
    "Alejandro Sarria"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The generalized Hunter-Saxton system comprises several well-known models from fluid dynamics and serves as a tool for the study of fluid convection and stretching in one-dimensional evolution equations. In this work, we examine the global regularity of periodic smooth solutions of this system in $L^p$, $p \\in [1,\\infty)$, spaces for nonzero real parameters $(\\lambda,\\kappa)$. Our results significantly improve/extend those by Wunsch et al. [27-29] and Sarria [21]. Furthermore, we study the effects that different boundary conditions have on the global regularity of solutions by replacing periodicity with a homogeneous three-point boundary condition and establish finite-time blowup of a local-in-time solution of the resulting system for particular values of the parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-11T23:41:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global regularity",
      "periodic smooth solutions",
      "one-dimensional evolution equations",
      "generalized hunter-saxton system comprises",
      "nonzero real parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}