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

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 |

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### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

### Cite this

**Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid.** / Shibata, Yoshihiro; Tanaka, Koumei.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 53, no. 3-4, pp. 605-623. https://doi.org/10.1016/j.camwa.2006.02.030

}

TY - JOUR

T1 - Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid

AU - Shibata, Yoshihiro

AU - Tanaka, Koumei

PY - 2007/2

Y1 - 2007/2

N2 - We consider a compressible viscous fluid affected by external forces of general form which are small and smooth enough in suitable norms in R3. 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 H3-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 H3 and also belong to L6 / 5.

AB - We consider a compressible viscous fluid affected by external forces of general form which are small and smooth enough in suitable norms in R3. 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 H3-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 H3 and also belong to L6 / 5.

KW - Compressible fluid

KW - Navier-Stokes equation

KW - Stability

KW - Stationary solution

UR - http://www.scopus.com/inward/record.url?scp=34247873112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247873112&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2006.02.030

DO - 10.1016/j.camwa.2006.02.030

M3 - Article

AN - SCOPUS:34247873112

VL - 53

SP - 605

EP - 623

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 3-4

ER -