{
  "id": "1110.0662",
  "version": "v1",
  "published": "2011-10-04T12:39:40.000Z",
  "updated": "2011-10-04T12:39:40.000Z",
  "title": "On the blowup and lifespan of smooth solutions to a class of 2-D nonlinear wave equations with small initial data",
  "authors": [
    "Jun Li",
    "Ingo Witt",
    "Huicheng Yin"
  ],
  "comment": "30 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We are concerned with a class of two-dimensional nonlinear wave equations $\\p_t^2u-\\div(c^2(u)\\na u)=0$ or $\\p_t^2u-c(u)\\div(c(u)\\na u)=0$ with small initial data $(u(0,x),\\p_tu(0,x))=(\\ve u_0(x), \\ve u_1(x))$, where $c(u)$ is a smooth function, $c(0)\\not =0$, $x\\in\\Bbb R^2$, $u_0(x), u_1(x)\\in C_0^{\\infty}(\\Bbb R^2)$ depend only on $r=\\sqrt{x_1^2+x_2^2}$, and $\\ve>0$ is sufficiently small. Such equations arise in a pressure-gradient model of fluid dynamics, also in a liquid crystal model or other variational wave equations. When $c'(0)\\not= 0$ or $c'(0)=0$, $c\"(0)\\not= 0$, we establish blowup and determine the lifespan of smooth solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-04T12:39:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35J70"
    ],
    "keywords": [
      "small initial data",
      "smooth solutions",
      "two-dimensional nonlinear wave equations",
      "variational wave equations",
      "liquid crystal model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.0662L"
    }
  }
}