{
  "id": "math-ph/9912009",
  "version": "v2",
  "published": "1999-12-13T11:31:05.000Z",
  "updated": "1999-12-17T10:49:14.000Z",
  "title": "Dispersion and collapse of wave maps",
  "authors": [
    "P. Bizoń",
    "T. Chmaj",
    "Z. Tabor"
  ],
  "comment": "14 pages, Latex, 9 eps figures included, typos corrected",
  "journal": "Nonlinearity 13 (2000) 1411-1423",
  "doi": "10.1088/0951-7715/13/4/323",
  "categories": [
    "math-ph",
    "gr-qc",
    "math.MP"
  ],
  "abstract": "We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behavior in formation of black holes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-12-17T10:49:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dispersion",
      "second conjecture states",
      "sufficiently large initial data",
      "equivariant wave maps",
      "first conjecture states"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}