### Abstract

We consider a compressible viscous fluid effected by general form external force in R^{3}. In part 1, an analysis of the linearized problem based on the weighted-L_{2} method implies a condition on the external force for the existence and some regularities of the steady flow. In part 2, we study the stability of the steady flow with respect to the initial disturbance. What we proved is: if H^{3}-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

Original language | English |
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Pages (from-to) | 797-826 |

Number of pages | 30 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 55 |

Issue number | 3 |

Publication status | Published - 2003 Jul |

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### Keywords

- Compressible fluid
- Navier-Stokes equation
- Stability
- Stationary solution

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Mathematical Society of Japan*,

*55*(3), 797-826.

**On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance.** / Shibata, Yoshihiro; Tanaka, Koumei.

Research output: Contribution to journal › Article

*Journal of the Mathematical Society of Japan*, vol. 55, no. 3, pp. 797-826.

}

TY - JOUR

T1 - On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance

AU - Shibata, Yoshihiro

AU - Tanaka, Koumei

PY - 2003/7

Y1 - 2003/7

N2 - We consider a compressible viscous fluid effected by general form external force in R3. In part 1, an analysis of the linearized problem based on the weighted-L2 method implies a condition on the external force for the existence and some regularities of the steady flow. In part 2, we study the stability of the steady flow with respect to the initial disturbance. What we proved is: if H3-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

AB - We consider a compressible viscous fluid effected by general form external force in R3. In part 1, an analysis of the linearized problem based on the weighted-L2 method implies a condition on the external force for the existence and some regularities of the steady flow. In part 2, we study the stability of the steady flow with respect to the initial disturbance. What we proved is: if H3-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

KW - Compressible fluid

KW - Navier-Stokes equation

KW - Stability

KW - Stationary solution

UR - http://www.scopus.com/inward/record.url?scp=0142118603&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142118603&partnerID=8YFLogxK

M3 - Article

VL - 55

SP - 797

EP - 826

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 3

ER -