{
  "id": "1412.4306",
  "version": "v1",
  "published": "2014-12-14T03:01:42.000Z",
  "updated": "2014-12-14T03:01:42.000Z",
  "title": "The Well-posedness and Blow-up rate of Solution for the Generalized Zakharov equations with Magnetic field in R^d",
  "authors": [
    "Xinglong Wu",
    "Boling Guo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The present paper is devoted to the study of the well-posedness and the lower bound of blow-up rate to the Cauchy problem of the generalized Zakharov(GZ) equations with magnetic field in R^d. The work of well-posedness of the GZ system bases on the local well-posedness theory in [9]. At first, the existence, uniqueness and continuity of solution to the GZ system with magnetic field in Rd is proved. Next, we establish the lower bound of blow-up rate of blow-up solution in sobolev spaces to the GZ system, which is almost a critical index. Finally, we obtain the long time behavior of global solution,whose H^k-norm grows at k-exponentially in time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-14T03:01:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "blow-up rate",
      "magnetic field",
      "generalized zakharov equations",
      "lower bound",
      "long time behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4306W"
    }
  }
}