## 抄録

We investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible Navier-Stokes equation in a half space. The main concern is to analyze the phenomena that happens when the fluid blows out through the boundary. Thus, it is natural to consider the problem in the Eulerian coordinate. We have obtained the two results for this problem. The first result is concerning the existence of the stationary solution. We present the necessary and sufficient condition which ensures the existence of the stationary solution. Then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable Sobolev space. The second result is proved by using an L^{2}-energy method with the aid of the Poincaré type inequality.

本文言語 | English |
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ページ（範囲） | 483-500 |

ページ数 | 18 |

ジャーナル | Communications in Mathematical Physics |

巻 | 240 |

号 | 3 |

DOI | |

出版ステータス | Published - 2003 9 |

外部発表 | はい |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics