### Abstract

The asymptotic behavior of the linearized semigroup at spatially periodic stationary solution of the compressible Navier–Stokes equation in a periodic layer of R^{n}(n= 2 , 3) is investigated. It is shown that if the Reynolds and Mach numbers are sufficiently small, then the linearized semigroup is decomposed into two parts; one behaves like a solution of an n- 1 dimensional linear heat equation as time goes to infinity and the other one decays exponentially.

Original language | English |
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Pages (from-to) | 739-772 |

Number of pages | 34 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 19 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 2017 |

### All Science Journal Classification (ASJC) codes

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics

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## Cite this

Enomoto, S., & Kagei, Y. (2017). Asymptotic Behavior of the Linearized Semigroup at Space-Periodic Stationary Solution of the Compressible Navier–Stokes Equation.

*Journal of Mathematical Fluid Mechanics*,*19*(4), 739-772. https://doi.org/10.1007/s00021-016-0304-3