{
  "id": "1912.11353",
  "version": "v1",
  "published": "2019-12-23T02:14:56.000Z",
  "updated": "2019-12-23T02:14:56.000Z",
  "title": "Almost Optimal Local Well-Posedness of the Chern-Simons-Dirac System in the Coulomb Gauge",
  "authors": [
    "Seokchang Hong",
    "Kiyeon Lee"
  ],
  "comment": "23 pages. arXiv admin note: text overlap with arXiv:1912.06790",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the Cauchy problem of regularity and uniqueness of the Chern-Simons-Dirac system in the Coulomb gauge for initial data in $B^0_{2,1}$. The novelty of this paper is on proving almost critical regularity by using the full localization of space-time Fourier side and bilinear estimates given by Selberg. We also prove the Dirac spinor flow of Chern-Simons-Dirac system cannot be $C^3$ at the origin in $H^s$ if $s<0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-23T02:14:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chern-simons-dirac system",
      "optimal local well-posedness",
      "coulomb gauge",
      "space-time fourier side",
      "dirac spinor flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}