{
  "id": "1803.05057",
  "version": "v1",
  "published": "2018-03-13T21:39:50.000Z",
  "updated": "2018-03-13T21:39:50.000Z",
  "title": "Low-regularity global well-posedness for the Klein-Gordon-Schrödinger system on $\\mathbb R^{+}$",
  "authors": [
    "E. Compaan",
    "N. Tzirakis"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we establish an almost optimal well-posedness and regularity theory for the Klein-Gordon-Schr\\\"odinger system on the half line. In particular we prove local-in-time well-posedness for rough initial data in Sobolev spaces of negative indices. Our results are consistent with the sharp well-posedness results that exist in the full line case and in this sense appear to be sharp. Finally we prove a global well-posedness result by combining the $L^2$ conservation law of the Schr\\\"odinger part with a careful iteration of the rough wave part in lower order Sobolev norms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-13T21:39:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35G25"
    ],
    "keywords": [
      "low-regularity global well-posedness",
      "klein-gordon-schrödinger system",
      "lower order sobolev norms",
      "rough initial data",
      "rough wave part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}