{
  "id": "2308.09692",
  "version": "v1",
  "published": "2023-08-18T17:38:04.000Z",
  "updated": "2023-08-18T17:38:04.000Z",
  "title": "Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise",
  "authors": [
    "Kazuo Yamazaki"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We study the two-dimensional magnetohydrodynamics system forced by space-time white noise. Due to a lack of an explicit invariant measure, the approach of Da Prato and Debussche (2002, J. Funct. Anal., \\textbf{196}, pp. 180--210) on the Navier-Stokes equations does not seem to fit. We follow instead the approach of Hairer and Rosati (2023, arXiv:2301.11059 [math.PR]), take advantage of the structure of Maxwell's equation, such as anti-symmetry, to find an appropriate paracontrolled ansatz and many crucial cancellations, and prove the global-in-time existence and uniqueness of its solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-18T17:38:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "space-time white noise",
      "two-dimensional magnetohydrodynamics system",
      "explicit invariant measure",
      "da prato",
      "global-in-time existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}