{
  "id": "1811.08791",
  "version": "v2",
  "published": "2018-11-21T15:42:39.000Z",
  "updated": "2018-11-28T18:37:50.000Z",
  "title": "The Chern-Simons-Higgs and the Chern-Simons-Dirac equations in Fourier-Lebesgue spaces",
  "authors": [
    "Hartmut Pecher"
  ],
  "comment": "18 pages, Proof of Lemma 2.1 modified",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The Chern-Simons-Higgs and the Chern-Simons-Dirac systems in Lorenz gauge are locally well-posed in suitable Fourier-Lebesgue spaces $\\hat{H}^{s,r}$. Our aim is to minimize $s=s(r)$ in the range $1<r \\le 2$ . If $r \\to 1$ we show that we almost reach the critical regularity dictated by scaling. In the classical case $r=2$ the results are due to Huh and Oh. Crucial is the fact that the decisive quadratic nonlinearities fulfill a null condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-11-28T18:37:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q40",
      "35L70"
    ],
    "keywords": [
      "chern-simons-dirac equations",
      "chern-simons-higgs",
      "decisive quadratic nonlinearities fulfill",
      "chern-simons-dirac systems",
      "lorenz gauge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}