### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Engineering(all)
- Applied Mathematics

### Cite this

*Japan Journal of Applied Mathematics*,

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

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

Research output: Contribution to journal › Article

*Japan Journal of Applied Mathematics*, vol. 1, no. 2, pp. 435-457. https://doi.org/10.1007/BF03167068

}

TY - JOUR

T1 - On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics

AU - Umeda, Tomio

AU - Kawashima, Shuichi

AU - Shizuta, Yasushi

PY - 1984/12/1

Y1 - 1984/12/1

N2 - 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.

AB - 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.

KW - decay of solutions

KW - hyperbolic-parabolic type

KW - linearized equations

KW - magnetohydrodynamics

UR - http://www.scopus.com/inward/record.url?scp=0011034308&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011034308&partnerID=8YFLogxK

U2 - 10.1007/BF03167068

DO - 10.1007/BF03167068

M3 - Article

AN - SCOPUS:0011034308

VL - 1

SP - 435

EP - 457

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 2

ER -