{
  "id": "math/0607458",
  "version": "v3",
  "published": "2006-07-19T09:42:00.000Z",
  "updated": "2008-01-12T05:46:22.000Z",
  "title": "On well-posedness of the Cauchy problem for MHD system in Besov spaces",
  "authors": [
    "Changxing Miao",
    "Baoquan Yuan"
  ],
  "comment": "23pages",
  "journal": "Math.Meth.Appl.Sci.32(2009)53-76",
  "doi": "10.1002/mma.1026",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is devoted to the study of the Cauchy problem of incompressible magneto-hydrodynamics system in framework of Besov spaces. In the case of spatial dimension $n\\ge 3$ we establish the global well-posedness of the Cauchy problem of incompressible magneto-hydrodynamics system for small data and the local one for large data in Besov space $\\dot{B}^{\\frac np-1}_{p,r}(\\mr^n)$, $1\\le p<\\infty$ and $1\\le r\\le\\infty$. Meanwhile, we also prove the weak-strong uniqueness of solutions with data in $\\dot{B}^{\\frac np-1}_{p,r}(\\mr^n)\\cap L^2(\\mr^n)$ for $\\frac n{2p}+\\frac2r>1$. In case of $n=2$, we establish the global well-posedness of solutions for large initial data in homogeneous Besov space $\\dot{B}^{\\frac2p-1}_{p,r}(\\mr^2)$ for $2< p<\\infty$ and $1\\le r<\\infty$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-01-12T05:46:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76W05",
      "74H20"
    ],
    "keywords": [
      "cauchy problem",
      "mhd system",
      "incompressible magneto-hydrodynamics system",
      "global well-posedness",
      "large initial data"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}