{
  "id": "0806.3592",
  "version": "v2",
  "published": "2008-06-22T21:32:39.000Z",
  "updated": "2009-08-06T00:09:47.000Z",
  "title": "Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class",
  "authors": [
    "Terence Tao"
  ],
  "comment": "77 pages, no figures. Will not be published in current form, pending future reorganisation of the heatwave project",
  "categories": [
    "math.AP"
  ],
  "abstract": "Using the harmonic map heat flow, we construct an energy class for wave maps $\\phi$ from two-dimensional Minkowski space $\\R^{1+2}$ to hyperbolic spaces $\\H^m$, and then show (conditionally on a large data well-posedness claim for such wave maps) that no stationary, travelling, self-similar, or degenerate wave maps exist in this energy class. These results form three of the five claims required in our earlier paper (arXiv:0805.4666) to prove global regularity for such wave maps. (The conditional claim of large data well-posedness is one of the remaining claims required in that paper.)",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-06T00:09:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70"
    ],
    "keywords": [
      "energy class",
      "global regularity",
      "self-similar solutions",
      "stationary",
      "harmonic map heat flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 77,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.3592T"
    }
  }
}