{
  "id": "1101.0713",
  "version": "v2",
  "published": "2011-01-04T12:25:16.000Z",
  "updated": "2011-06-10T10:08:49.000Z",
  "title": "Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres",
  "authors": [
    "Paweł Biernat",
    "Piotr Bizoń"
  ],
  "comment": "24 pages, 8 figures, minor corrections, matches published version",
  "journal": "Nonlinearity 24 (2011) 2211-2228",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Using mixed analytical and numerical methods we investigate the development of singularities in the heat flow for corotational harmonic maps from the $d$-dimensional sphere to itself for $3\\leq d\\leq 6$. By gluing together shrinking and expanding asymptotically self-similar solutions we construct global weak solutions which are smooth everywhere except for a sequence of times $T_1<T_2<...<T_k<\\infty$ at which there occurs the type I blow-up at one of the poles of the sphere. We show that in the generic case the continuation beyond blow-up is unique, the topological degree of the map changes by one at each blow-up time $T_i$, and eventually the solution comes to rest at the zero energy constant map.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-10T10:08:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat flow",
      "generic blowup",
      "unique continuation",
      "zero energy constant map",
      "construct global weak solutions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/24/8/005",
      "journal": "Nonlinearity",
      "year": 2011,
      "month": "Aug",
      "volume": 24,
      "number": 8,
      "pages": 2211
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011Nonli..24.2211B"
    }
  }
}