{
  "id": "2411.06748",
  "version": "v1",
  "published": "2024-11-11T06:57:14.000Z",
  "updated": "2024-11-11T06:57:14.000Z",
  "title": "Global Well-posedness and Long-time Behavior of the General Ericksen--Leslie System in 2D under a Magnetic Field",
  "authors": [
    "Qingtong Wu"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we investigate the global well-posedness and long-time behavior of the general Ericksen--Leslie system in 2D under a magnetic field. The PDE system consists of Navier--Stokes equations and kinematic transport equations for the orientations of liquid crystal molecules. For liquid crystal molecules with fixed modulus in torus $\\mathbb{T}^2$, we prove the well-posedness of steady-state solutions in order to prove that there exist global strong solutions to the general Ericksen--Leslie system, which are smooth away from the initial time, and the long-time behavior of the solutions is classified according to the $\\mathbb{T}^2$ boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-11T06:57:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general ericksen-leslie system",
      "long-time behavior",
      "magnetic field",
      "global well-posedness",
      "liquid crystal molecules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}