### Abstract

The linearized problem for the compressible Navier-Stokes equation around a given con- stant state is considered in a periodic layer of ℝ^{n} with n ≥ 2, and spectral properties of the linearized semigroup are investigated. It is shown that the linearized operator gener- ates a C_{0}-semigroup in L^{2} over the periodic layer and the time-asymptotic leading part of the semigroup is given by a C_{0}-semigroup generated by an n – 1-dimensional elliptic operator with constant coefficients that are determined by solutions of a Stokes system over the basic period domain.

Original language | English |
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Pages (from-to) | 337-372 |

Number of pages | 36 |

Journal | Publications of the Research Institute for Mathematical Sciences |

Volume | 51 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)