{
  "id": "1707.02719",
  "version": "v1",
  "published": "2017-07-10T07:13:46.000Z",
  "updated": "2017-07-10T07:13:46.000Z",
  "title": "Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field",
  "authors": [
    "Sigmund Selberg"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove global well-posedness for the coupled Maxwell-Dirac-Thirring-Gross-Neveu equations in one space dimension, with data for the Dirac spinor in the critical space $L^2(\\R)$. In particular, we recover earlier results of Candy and Huh for the Thirring and Gross-Neveu models, respectively, without the coupling to the electromagnetic field, but the function spaces we introduce allow for a greatly simplified proof. We also apply our method to prove local well-posedness in $L^2(\\R)$ for a quadratic Dirac equation, improving an earlier result of Tesfahun and the author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-10T07:13:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gross-neveu models",
      "electromagnetic field",
      "critical space",
      "global existence",
      "earlier result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}