{
  "id": "1605.07113",
  "version": "v1",
  "published": "2016-05-23T17:37:01.000Z",
  "updated": "2016-05-23T17:37:01.000Z",
  "title": "Global Existence for a Nonlinear System with Fractional Laplacian in Banach Space",
  "authors": [
    "Miguel Loayza",
    "Paulo R. F. S. Silva"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the cauchy problem for the fractional power dissipative equation $u_t+(-\\Delta )^{\\beta/2} u=F(u)$, where $\\beta>0$ and $F(u)=B(u, ...,u)$ and $B$ is a multilinear form on a Banach space $E$. We show a global existence result assuming some properties of scaling degree of the multilinear form and the norm of the space $E$. We extend the ideas used for the treating of the equation to determine the global existence for the system $u_t+(-\\Delta)^{\\beta/2}= F(v)$, $v_t+(-\\Delta )^{\\beta/2}v=G(u)$ where $F(u)=B_1(u,...,u), G(v)=B_2(v,...,v)$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-23T17:37:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach space",
      "nonlinear system",
      "fractional laplacian",
      "multilinear form",
      "fractional power dissipative equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}