{
  "id": "1209.3841",
  "version": "v1",
  "published": "2012-09-18T03:56:29.000Z",
  "updated": "2012-09-18T03:56:29.000Z",
  "title": "Low regularity solutions to the Chern-Simons-Dirac and the Chern-Simons-Higgs equations in the Lorenz gauge",
  "authors": [
    "Hyungjin Huh",
    "Sung-Jin Oh"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we address the problem of local well-posedness of the Chern-Simons-Dirac (CSD) and the Chern-Simons-Higgs (CSH) equations in the Lorenz gauge for low regularity initial data. One of our main contributions is the uncovering of a null structure of (CSD). Combined with the standard machinery of $X^{s,b}$ spaces, we obtain local well-posedness of (CSD) for initial data $a_{\\mu}, \\psi \\in H^{1/4+\\epsilon}_{x}$. Moreover, it is observed that the same techniques applied to (CSH) lead to a quick proof of local well-posedness for initial data $a_{\\mu} \\in H^{1/4+\\epsilon}_{x}$, $(\\phi, \\partial_{t} \\phi) \\in H^{3/4+\\epsilon}_{x} \\times H^{-1/4+\\epsilon}_{x}$, which improves the previous result of Selberg-Tesfahun (2012).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-18T03:56:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low regularity solutions",
      "lorenz gauge",
      "chern-simons-higgs equations",
      "local well-posedness",
      "chern-simons-dirac"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1186657,
      "adsabs": "2012arXiv1209.3841H"
    }
  }
}