{
  "id": "2211.03056",
  "version": "v1",
  "published": "2022-11-06T08:02:57.000Z",
  "updated": "2022-11-06T08:02:57.000Z",
  "title": "Strong solutions of the Landau-Lifshitz-Bloch equation in Besov space",
  "authors": [
    "Yi Peng",
    "Huaqiao Wang"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We focus on the existence and uniqueness of the three-dimensional Landau-Lifshitz-Bloch equation supplemented with the initial data in Besov space $\\dot{B}_{2,1}^{\\frac{3}{2}}$. Utilizing a new commutator estimate, we establish the local existence and uniqueness of strong solutions for any initial data in $\\dot{B}_{2,1}^{\\frac{3}{2}}$. When the initial data is small enough in $\\dot{B}_{2,1}^{\\frac{3}{2}}$, we obtain the global existence and uniqueness. Furthermore, we also establish a blow-up criterion of the solution to the Landau-Lifshitz-Bloch equation and then we prove the global existence of strong solutions in Sobolev space under a new condition based on the blow-up criterion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-06T08:02:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82D40",
      "35K10",
      "35K59",
      "35D35"
    ],
    "keywords": [
      "strong solutions",
      "besov space",
      "initial data",
      "blow-up criterion",
      "global existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}