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

  • Tomio Umeda
  • Shuichi Kawashima
  • Yasushi Shizuta


The linearized equations of the electrically conducting compressible viscous fluids are studied. It is shown that the decay estimate (1+t)−3/4 inL 2(R 3) holds for solutions of the above equations, provided that the initial data are inL 2(R 3)∩L 1(R 3). 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.

Key words

magnetohydrodynamics decay of solutions linearized equations hyperbolic-parabolic type 


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Copyright information

© JJAM Publishing Committee 1984

Authors and Affiliations

  • Tomio Umeda
    • 1
  • Shuichi Kawashima
    • 2
  • Yasushi Shizuta
    • 2
  1. 1.Department of MathematicsOsaka UniversityOsakaJapan
  2. 2.Department of MathematicsNara Women’s UniversityNaraJapan

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