{
  "id": "1912.09194",
  "version": "v1",
  "published": "2019-12-19T13:53:19.000Z",
  "updated": "2019-12-19T13:53:19.000Z",
  "title": "The Global Solvability Of The Hall-magnetohydrodynamics System In Critical Sobolev Spaces",
  "authors": [
    "Raphaël Danchin",
    "Jin Tan"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We are concerned with the 3D incompressible Hall-magnetohydro-dynamic system (Hall-MHD). Our first aim is to provide the reader with an elementary proof of a global well-posedness result for small data with critical Sobolev regularity, in the spirit of Fujita-Kato's theorem [10] for the Navier-Stokes equations. Next, we investigate the long-time asymptotics of global solutions of the Hall-MHD system that are in the Fujita-Kato regularity class. A weak-strong uniqueness statement is also proven. Finally, we consider the so-called 2 1/2 D flows for the Hall-MHD system, and prove the global existence of strong solutions, assuming only that the initial magnetic field is small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-19T13:53:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical sobolev spaces",
      "global solvability",
      "hall-magnetohydrodynamics system",
      "hall-mhd system",
      "3d incompressible hall-magnetohydro-dynamic system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}