{
  "id": "1910.13879",
  "version": "v1",
  "published": "2019-10-29T10:51:17.000Z",
  "updated": "2019-10-29T10:51:17.000Z",
  "title": "On the Global Strong Solutions to Magnetohydrodynamics with Density-Dependent Viscosity and Degenerate Heat-Conductivity in Unbounded Domains",
  "authors": [
    "Yuebo Cao",
    "Yi Peng",
    "Ying Sun"
  ],
  "comment": "19 pages. arXiv admin note: substantial text overlap with arXiv:1809.04451, arXiv:1910.05579; text overlap with arXiv:1809.00609 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "For the equations of a planar magnetohydrodynamic (MHD) compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity being proportional to a positive power of the temperature, we obtain global existence of the unique strong solutions to the Cauchy problem or the initial-boundary-value one under natural conditions on the initial data in one-dimensional unbounded domains. Our result generalizes the classical one of the compressible Navier-Stokes system with constant viscosity and heat conductivity ([Kazhikhov. Siberian Math. J. (1982)]) to the planar MHD compressible flow with nonlinear viscosity and degenerate heat-conductivity, which means no shock wave, vacuum, or mass or heat concentration will be developed in finite time, although the interaction between the magnetodynamic effects and hydrodynamic is complex and the motion of the flow has large oscillations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-29T10:51:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global strong solutions",
      "degenerate heat-conductivity",
      "unbounded domains",
      "density-dependent viscosity",
      "magnetohydrodynamic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}