Smooth global solutions for two-dimensional equations of electro-magneto-fluid dynamics

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Abstract

The equations of an electrically conducting compressible fluid in electro-magneto-fluid dynamics are studied. It is proved that in a certain case of two-dimensional flow, the equations of the fluid become a symmetric hyperbolic-parabolic system in both of the viscous and non-viscous cases. Therefore, the initial value problem is well posed in the Sobolev spaces at least for short time interval. Furthermore, in the viscous case, the solution exists globally in time and tends to the constant state as time goes to infinity, provided the initial data are closed to the constant state. The proof is based on a technical energy method, which makes use of a quadratic function associated with the total energy of the fluid.

Original languageEnglish
Pages (from-to)207-222
Number of pages16
JournalJapan Journal of Applied Mathematics
Volume1
Issue number1
DOIs
Publication statusPublished - 1984 Sep 1
Externally publishedYes

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Keywords

  • electro-magneto-fluid dynamics
  • energy method
  • global existence
  • symmetric hyperbolic-parabolic type
  • two-dimensional equations

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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