### Abstract

The resolvent problem of the linearized compressible Navier-Stokes equation around a given constant state is considered in an infinite layer [formula omitted], under the no slip boundary condition for the momentum. It is proved that the linearized operator is sectorial in [formula omitted]for [formula omitted]. The L_{p}estimates for the resolvent are established for all [formula omitted]. The estimates for the high frequency part of the resolvent are also derived, which lead to the exponential decay of the corresponding part of the semigroup.

Original language | English |
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Pages (from-to) | 287-337 |

Number of pages | 51 |

Journal | Funkcialaj Ekvacioj |

Volume | 50 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Kagei, Y. (2007). Resolvent Estimates for the Linearized Compressible Navier-Stokes Equation in an Infinite Layer.

*Funkcialaj Ekvacioj*,*50*(2), 287-337. https://doi.org/10.1619/fesi.50.287