{
  "id": "2109.13657",
  "version": "v2",
  "published": "2021-09-28T12:18:00.000Z",
  "updated": "2022-09-22T17:03:21.000Z",
  "title": "Global Well-Posedness For Half-Wave Maps With $S^2$ and $\\mathbb{H}^2$ Targets For Small Smooth Initial Data",
  "authors": [
    "Yang Liu"
  ],
  "comment": "48 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove global well-posedness for the half-wave map with $S^2$ target for small $\\dot{H}^{\\frac{n}{2}} \\times \\dot{H}^{\\frac{n}{2}-1}$ initial data. We also prove the global well-posedness for the equation with $\\mathbb{H}^2$ target for small smooth $\\dot{B}^{\\frac{n}{2}}_{2,1} \\times \\dot{B}^{\\frac{n}{2}-1}_{2,1}$ initial data.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-09-22T17:03:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35A01",
      "35B40"
    ],
    "keywords": [
      "small smooth initial data",
      "global well-posedness",
      "half-wave map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}