{
  "id": "1701.03083",
  "version": "v1",
  "published": "2017-01-11T18:05:02.000Z",
  "updated": "2017-01-11T18:05:02.000Z",
  "title": "The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions",
  "authors": [
    "Susana Gutiérrez",
    "André de Laire"
  ],
  "comment": "40 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a global well-posedness result for the Landau-Lifshitz equation with Gilbert damping provided that the BMO semi-norm of the initial data is small. As a consequence, we deduce the existence of self-similar solutions in any dimension. In the one-dimensional case, we characterize the self-similar solutions associated with an initial data given by some ($\\mathbb{S}^2$-valued) step function and establish their stability. We also show the existence of multiple solutions if the damping is strong enough. Our arguments rely on the study of a dissipative quasilinear Schr\\\"odinger obtained via the stereographic projection and techniques introduced by Koch and Tataru.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-11T18:05:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R05",
      "35Q60",
      "35A01",
      "35C06",
      "35B35",
      "35Q55",
      "35Q56",
      "35A02",
      "53C44"
    ],
    "keywords": [
      "self-similar solutions",
      "landau-lifshitz-gilbert equation",
      "cauchy problem",
      "initial data",
      "global well-posedness result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}