{
  "id": "1205.3615",
  "version": "v1",
  "published": "2012-05-16T09:46:12.000Z",
  "updated": "2012-05-16T09:46:12.000Z",
  "title": "On the Cauchy problem for Hartree equation in the Wiener algebra",
  "authors": [
    "Rémi Carles",
    "Lounes Mouzaoui"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the mass-subcritical Hartree equation with a homogeneous kernel, in the space of square integrable functions whose Fourier transform is integrable. We prove a global well-posedness result in this space. On the other hand, we show that the Cauchy problem is not even locally well-posed if we simply work in the space of functions whose Fourier transform is integrable. Similar results are proven when the kernel is not homogeneous, and is such that its Fourier transform belongs to some Lebesgue space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-16T09:46:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cauchy problem",
      "wiener algebra",
      "fourier transform belongs",
      "global well-posedness result",
      "square integrable functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3615C"
    }
  }
}