{
  "id": "1210.2056",
  "version": "v1",
  "published": "2012-10-07T13:47:51.000Z",
  "updated": "2012-10-07T13:47:51.000Z",
  "title": "A Large Data Regime for non-linear Wave Equations",
  "authors": [
    "Jinhua Wang",
    "Pin Yu"
  ],
  "comment": "44 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1207.5591",
  "categories": [
    "math.AP"
  ],
  "abstract": "For semi-linear wave equations with null form non-linearities on $\\mathbb{R}^{3+1}$, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also exhibit a set of localized data for which the corresponding solutions are strongly focused, which in geometric terms means that a wave travels along an specific incoming null geodesic in such a way that almost all of the energy is confined in a tubular neighborhood of the geodesic and almost no energy radiating out of this tubular neighborhood.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-07T13:47:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large data regime",
      "non-linear wave equations",
      "tubular neighborhood",
      "specific incoming null geodesic",
      "semi-linear wave equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.2056W"
    }
  }
}