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

Shuichi Kawashima

Research output: Contribution to journalArticle

59 Citations (Scopus)

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 - Sep 1 1984

Fingerprint

Global Smooth Solution
Fluid Dynamics
Fluid dynamics
Fluids
Fluid
Sobolev spaces
Initial value problems
Compressible Fluid
Parabolic Systems
Energy Method
Hyperbolic Systems
Quadratic Function
Sobolev Spaces
Initial Value Problem
Infinity
Tend
Closed
Interval
Energy

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

Cite this

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

In: Japan Journal of Applied Mathematics, Vol. 1, No. 1, 01.09.1984, p. 207-222.

Research output: Contribution to journalArticle

@article{d918a698bacc4b55a6c2c9b5fc3cff02,
title = "Smooth global solutions for two-dimensional equations of electro-magneto-fluid dynamics",
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.",
author = "Shuichi Kawashima",
year = "1984",
month = "9",
day = "1",
doi = "10.1007/BF03167869",
language = "English",
volume = "1",
pages = "207--222",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "1",

}

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.

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 -