{
  "id": "1411.3115",
  "version": "v1",
  "published": "2014-11-12T09:57:13.000Z",
  "updated": "2014-11-12T09:57:13.000Z",
  "title": "Critical exponent for evolution equation in Modulation space",
  "authors": [
    "Huang Qiang",
    "Fan Dashan",
    "Chen Jiecheng"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we propose a method to find the critical exponent for certain evolution equations in modulation spaces. We define an index $\\sigma (s,q)$, and use it to determine the critical exponent of the fractional heat equation as an example. We prove that when $\\sigma (s,q)$ is greater than the critical exponent, this equation is locally well posed in the space $C(0,T;M_{p,q}^{s})$; and when $\\sigma (s,q)$ is less than the critical exponent, this equation is ill-posed in the space $C(0,T;M_{2,q}^{s})$. Our method may further be applied to some other evolution equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-12T09:57:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35A02",
      "42B37"
    ],
    "keywords": [
      "critical exponent",
      "evolution equation",
      "modulation space",
      "fractional heat equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}