{
  "id": "2307.06587",
  "version": "v1",
  "published": "2023-07-13T07:11:02.000Z",
  "updated": "2023-07-13T07:11:02.000Z",
  "title": "Weak solutions to the Hall-MHD equations whose singular sets in time have Hausdorff dimension strictly less than 1",
  "authors": [
    "Yi Peng",
    "Huaqiao Wang"
  ],
  "comment": "39 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we focus on the three-dimensional hyper viscous and resistive Hall-MHD equations on the torus, where the viscous and resistive exponent $\\alpha\\in [\\rho, 5/4)$ with a fixed constant $\\rho\\in (1,5/4)$. We prove the non-uniqueness of a class of weak solutions to the Hall-MHD equations, which have bounded kinetic energy and are smooth in time outside a set whose Hausdorff dimension strictly less than 1. The proof is based on the construction of the non-Leray-Hopf weak solutions via a convex integration scheme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-13T07:11:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hausdorff dimension",
      "singular sets",
      "non-leray-hopf weak solutions",
      "convex integration scheme",
      "time outside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}