{
  "id": "0908.1201",
  "version": "v1",
  "published": "2009-08-09T00:33:28.000Z",
  "updated": "2009-08-09T00:33:28.000Z",
  "title": "A construction of blow up solutions for co-rotational wave maps",
  "authors": [
    "Catalin I. Carstea"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The existence of co-rotational finite time blow up solutions to the wave map problem from R^{2+1} into N, where N is a surface of revolution with metric d\\rho^2+g(\\rho)^2 d\\theta^2, g an entire function, is proven. These are of the form u(t,r)=Q(\\lambda(t)t)+R(t,r), where Q is a time independent solution of the co-rotational wave map equation -u_{tt}+u_{rr}+r^{-1}u_r=r^{-2}g(u)g'(u), \\lambda(t)=t^{-1-\\nu}, \\nu>1/2 is arbitrary, and R is a term whose local energy goes to zero as t goes to 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-09T00:33:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35Q75",
      "35P25"
    ],
    "keywords": [
      "construction",
      "co-rotational finite time blow",
      "co-rotational wave map equation",
      "time independent solution",
      "wave map problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-010-1118-4",
      "journal": "Communications in Mathematical Physics",
      "year": 2010,
      "month": "Dec",
      "volume": 300,
      "number": 2,
      "pages": 487
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CMaPh.300..487C"
    }
  }
}