{
  "id": "0804.4301",
  "version": "v1",
  "published": "2008-04-27T22:35:17.000Z",
  "updated": "2008-04-27T22:35:17.000Z",
  "title": "Null structure and almost optimal local well-posedness of the Maxwell-Dirac system",
  "authors": [
    "Piero D'Ancona",
    "Damiano Foschi",
    "Sigmund Selberg"
  ],
  "comment": "53 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We uncover the full null structure of the Maxwell-Dirac system in Lorenz gauge. This structure, which cannot be seen in the individual component equations, but only when considering the system as a whole, is expressed in terms of tri- and quadrilinear integral forms with cancellations measured by the angles between spatial frequencies. In the 3D case, we prove frequency-localized $L^2$ space-time estimates for these integral forms at the scale invariant regularity up to a logarithmic loss, hence we obtain almost optimal local well-posedness of the system by iteration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-27T22:35:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q40",
      "35L70"
    ],
    "keywords": [
      "optimal local well-posedness",
      "maxwell-dirac system",
      "individual component equations",
      "quadrilinear integral forms",
      "scale invariant regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.4301D"
    }
  }
}