On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics

Tomio Umeda, Shuichi Kawashima, Yasushi Shizuta

Research output: Contribution to journalArticle

122 Citations (Scopus)

Abstract

The linearized equations of the electrically conducting compressible viscous fluids are studied. It is shown that the decay estimate (1+t)-3/4 in L2(R3) holds for solutions of the above equations, provided that the initial data are in L2(R3)∩L1(R3). Since the systems of equations are not rotationally invariant, the perturbation theory for one parameter family of matrices is not useful enough to derive the above result. Therefore, by exploiting an energy method, we show that the decay estimate holds for the solutions of a general class of equations of symmetric hyperbolic-parabolic type, which contains the linearized equations in both electro-magneto-fluid dynamics and magnetohydrodynamics.

Original languageEnglish
Pages (from-to)435-457
Number of pages23
JournalJapan Journal of Applied Mathematics
Volume1
Issue number2
DOIs
Publication statusPublished - Dec 1 1984

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Decay of Solutions
Magnetohydrodynamics
Fluid Dynamics
Fluid dynamics
Fluids
Decay Estimates
Compressible Fluid
Energy Method
Viscous Fluid
Perturbation Theory
System of equations
Invariant

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

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On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics. / Umeda, Tomio; Kawashima, Shuichi; Shizuta, Yasushi.

In: Japan Journal of Applied Mathematics, Vol. 1, No. 2, 01.12.1984, p. 435-457.

Research output: Contribution to journalArticle

Umeda, Tomio ; Kawashima, Shuichi ; Shizuta, Yasushi. / On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics. In: Japan Journal of Applied Mathematics. 1984 ; Vol. 1, No. 2. pp. 435-457.
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