{
  "id": "math/0011173",
  "version": "v3",
  "published": "2000-11-22T11:35:41.000Z",
  "updated": "2001-01-10T22:37:15.000Z",
  "title": "Global regularity of wave maps II. Small energy in two dimensions",
  "authors": [
    "Terence Tao"
  ],
  "comment": "109 pages, no figures, submitted to Comm. Math. Phys. A technical error (U and phi need to be measured in slightly different spaces for induction purposes) has been corrected, and some other small errors fixed",
  "doi": "10.1007/PL00005588",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that wave maps from Minkowski space $\\R^{1+n}$ to a sphere $S^{m-1}$ are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space $\\dot H^{n/2}$, in all dimensions $n \\geq 2$. This generalizes the results in the prequel [math.AP/0010068] of this paper, which addressed the high-dimensional case $n \\geq 5$. In particular, in two dimensions we have global regularity whenever the energy is small, and global regularity for large data is thus reduced to demonstrating non-concentration of energy.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2001-01-10T22:37:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10"
    ],
    "keywords": [
      "global regularity",
      "wave maps",
      "small energy",
      "dimensions",
      "large data"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Communications in Mathematical Physics",
      "year": 2001,
      "volume": 224,
      "number": 2,
      "pages": 443
    },
    "note": {
      "typesetting": "TeX",
      "pages": 109,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001CMaPh.224..443T"
    }
  }
}