{
  "id": "1502.02611",
  "version": "v1",
  "published": "2015-02-09T19:19:29.000Z",
  "updated": "2015-02-09T19:19:29.000Z",
  "title": "Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation",
  "authors": [
    "Alberto Bressan",
    "Geng Chen"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The paper is concerned with conservative solutions to the nonlinear wave equation $u_{tt} - c(u)\\big(c(u) u_x\\big)_x = 0$. For an open dense set of $C^3$ initial data, we prove that the solution is piecewise smooth in the $t$-$x$ plane, while the gradient $u_x$ can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-09T19:19:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear wave equation",
      "conservative solutions",
      "generic regularity",
      "thoms transversality theorem",
      "open dense set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}