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

Shuichi Kawashima

Research output: Contribution to journalArticlepeer-review

78 Citations (Scopus)


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
Issue number1
Publication statusPublished - Sept 1 1984

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics


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