### 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 L^{2}(R^{3}) holds for solutions of the above equations, provided that the initial data are in L^{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.

Original language | English |
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Pages (from-to) | 435-457 |

Number of pages | 23 |

Journal | Japan Journal of Applied Mathematics |

Volume | 1 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1984 Dec 1 |

### Keywords

- decay of solutions
- hyperbolic-parabolic type
- linearized equations
- magnetohydrodynamics

### ASJC Scopus subject areas

- Engineering(all)
- Applied Mathematics

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## Cite this

*Japan Journal of Applied Mathematics*,

*1*(2), 435-457. https://doi.org/10.1007/BF03167068