{
  "id": "1412.5679",
  "version": "v1",
  "published": "2014-12-17T23:49:20.000Z",
  "updated": "2014-12-17T23:49:20.000Z",
  "title": "On the global stability of the wave-map equation in Kerr spaces with small angular momentum",
  "authors": [
    "A. D. Ionescu",
    "S. Klainerman"
  ],
  "categories": [
    "math.AP",
    "gr-qc"
  ],
  "abstract": "This paper is motivated by the problem of the nonlinear stability of the Kerr solution for axially symmetric perturbations. We consider a model problem concerning the axially symmetric perturbations of a wave map $\\Phi$ defined from a fixed Kerr solution $\\KK(M,a)$, $0\\le a < M $, with values in the two dimensional hyperbolic space $\\HHH^2$. A particular such wave map is given by the complex Ernst potential associated to the axial Killing vectorfield $\\Z$ of $\\KK(M,a)$. We conjecture that this stationary solution is stable, under small axially symmetric perturbations, in the domain of outer communication (DOC) of $\\KK(M,a)$, for all $0\\le a<M$ and we provide preliminary support for its validity, by deriving convincing stability estimates for the linearized system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-17T23:49:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small angular momentum",
      "wave-map equation",
      "global stability",
      "kerr spaces",
      "kerr solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1334920,
      "adsabs": "2014arXiv1412.5679I"
    }
  }
}