{
  "id": "2005.14130",
  "version": "v1",
  "published": "2020-05-28T16:25:44.000Z",
  "updated": "2020-05-28T16:25:44.000Z",
  "title": "Low regularity of non-$L^2(R^n)$ local solutions to gMHD-alpha systems",
  "authors": [
    "Lorenzo Riva",
    "Nathan Pennington"
  ],
  "comment": "17 pages",
  "journal": "Electron. J. Differential Equations, Vol. 2020 (2020), No. 54",
  "categories": [
    "math.AP"
  ],
  "abstract": "The Magneto-Hydrodynamic (MHD) system of equations governs viscous fluids subject to a magnetic field and is derived via a coupling of the Navier-Stokes equations and Maxwell's equations. Recently it has become common to study generalizations of fluids-based differential equations. Here we consider the generalized Magneto-Hydrodynamic alpha (gMHD-$\\alpha$) system, which differs from the original MHD system by including an additional non-linear terms (indexed by $\\alpha$), and replacing the Laplace operators by more general Fourier multipliers with symbols of the form $-|\\xi|^\\gamma / g(|\\xi|)$. In a paper by Pennington, the problem was considered with initial data in the Sobolev space $H^{s,2}(\\mathbb{R}^n)$ with $n \\geq 3$. Here we consider the problem with initial data in $H^{s,p}(\\mathbb{R}^n)$ with $n \\geq 3$ and $p > 2$. Our goal is to minimize the regularity required for obtaining uniqueness of a solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-28T16:25:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35A02",
      "76W05"
    ],
    "keywords": [
      "local solutions",
      "gmhd-alpha systems",
      "low regularity",
      "initial data",
      "equations governs viscous fluids subject"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}