{
  "id": "2111.14835",
  "version": "v2",
  "published": "2021-11-29T08:17:53.000Z",
  "updated": "2022-04-12T02:33:28.000Z",
  "title": "Smooth local solutions to the Schrödinger flow for maps from a smooth bounded domain $Ω\\subset \\mathbb{R}^3$ into $\\mathbb{S}^2$",
  "authors": [
    "Bo Chen",
    "Youde Wang"
  ],
  "comment": "Some typos have been corrected in this version, and any comments are welcome. arXiv admin note: text overlap with arXiv:2111.14077",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we show the existence and uniqueness of short-time very regular or smooth solution to the initial-Neumann boundary value problem of the Schr\\\"{o}dinger flow for maps from a smooth bounded domain $\\Omega\\subset \\mathbb{R}^3$ into $\\mathbb{S}^2$ in the scale of Sobolev spaces. We provide a precise description of the compatibility conditions at the boundary for the initial data.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-12T02:33:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth bounded domain",
      "smooth local solutions",
      "schrödinger flow",
      "initial-neumann boundary value problem",
      "smooth solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}