### 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 language | English |
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Pages (from-to) | 207-222 |

Number of pages | 16 |

Journal | Japan Journal of Applied Mathematics |

Volume | 1 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1984 Sep 1 |

Externally published | Yes |

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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

### Cite this

**Smooth global solutions for two-dimensional equations of electro-magneto-fluid dynamics.** / Kawashima, Shuichi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Smooth global solutions for two-dimensional equations of electro-magneto-fluid dynamics

AU - Kawashima, Shuichi

PY - 1984/9/1

Y1 - 1984/9/1

N2 - 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.

AB - 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.

KW - electro-magneto-fluid dynamics

KW - energy method

KW - global existence

KW - symmetric hyperbolic-parabolic type

KW - two-dimensional equations

UR - http://www.scopus.com/inward/record.url?scp=77951514005&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951514005&partnerID=8YFLogxK

U2 - 10.1007/BF03167869

DO - 10.1007/BF03167869

M3 - Article

AN - SCOPUS:77951514005

VL - 1

SP - 207

EP - 222

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 1

ER -