### Abstract

We consider a compressible viscous fluid affected by external forces of general form which are small and smooth enough in suitable norms in R^{3}. In Shibata and Tanaka [Y. Shibata, K. Tanaka, On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance, J. Math. Soc. Japan 55 (2003) 797-826], we proved the unique existence and some regularity of the steady flow and its globally in-time stability with respect to a small initial disturbance in the H^{3}-framework. In this paper, we investigate the rate of the convergence of the non-stationary flow to the corresponding steady flow when the initial data are small enough in the H^{3} and also belong to L_{6 / 5}.

Original language | English |
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Pages (from-to) | 605-623 |

Number of pages | 19 |

Journal | Computers and Mathematics with Applications |

Volume | 53 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2007 Feb 1 |

### Keywords

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

### ASJC Scopus subject areas

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics