### Abstract

We report our results [5, 6, 7] concerning a global in time unique existence theorem of strong solutions to the equation describing the motion of compressible viscous fluid flow in a 2-dimensional exterior domain for small initial data and some decay properties of the analytic semigroup associated with Stokes operator of compressible viscous fluid flow in a 2-dimensional exterior domain. Our results are an extension of the works due to Matsumura and Nishida [13] and Kobayashi and Shibata [10] in a 3-dimensional exterior domain to the 2-dimensional case. We also discuss some analytic semigroup approach to the compressible viscous fluid flow in a bounded domain, which was first investigated by G. S trömer [20, 21, 22].

Original language | English |
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Title of host publication | Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 2010 |

Editors | Wolfgang Arendt, Jussi Behrndt, Volker Mehrmann, Karl-Heinz Förster, Joseph A. Ball, Carsten Trunk |

Publisher | Springer International Publishing |

Pages | 305-321 |

Number of pages | 17 |

ISBN (Print) | 9783034802963 |

Publication status | Published - 2012 Jan 1 |

Externally published | Yes |

Event | 21st International Workshop on Operator Theory and Applications, 2010 - Berlin, Germany Duration: 2010 Jul 12 → 2010 Jul 16 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 221 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Other

Other | 21st International Workshop on Operator Theory and Applications, 2010 |
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Country | Germany |

City | Berlin |

Period | 10/7/12 → 10/7/16 |

### Keywords

- 2-dimensional exterior domain
- Global in time unique existence theorem
- L-L decay estimate
- Local energy decay

### ASJC Scopus subject areas

- Analysis

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## Cite this

*Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 2010*(pp. 305-321). (Operator Theory: Advances and Applications; Vol. 221). Springer International Publishing.