### Abstract

Asymptotic behavior of solutions to the linearized compressible Navier-Stokes equation around a given constant state is considered in an infinite layer R^{n-1} x (0, a), n ≥ 2, under the no slip boundary condition for the momentum. The L^{P} decay estimates of the associated semigroup are established for all 1 ≤ p ≤ ∞. It is also shown that the time-asymptotic leading part of the semigroup is given by an n -1 dimensional heat semigroup.

Original language | English |
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Pages (from-to) | 763-794 |

Number of pages | 32 |

Journal | Publications of the Research Institute for Mathematical Sciences |

Volume | 43 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**Asymptotic behavior of the semigroup associated with the linearized compressible Navier-Stokes equation in an infinite layer.** / Kagei, Yoshiyuki.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Asymptotic behavior of the semigroup associated with the linearized compressible Navier-Stokes equation in an infinite layer

AU - Kagei, Yoshiyuki

PY - 2007/9/1

Y1 - 2007/9/1

N2 - Asymptotic behavior of solutions to the linearized compressible Navier-Stokes equation around a given constant state is considered in an infinite layer Rn-1 x (0, a), n ≥ 2, under the no slip boundary condition for the momentum. The LP decay estimates of the associated semigroup are established for all 1 ≤ p ≤ ∞. It is also shown that the time-asymptotic leading part of the semigroup is given by an n -1 dimensional heat semigroup.

AB - Asymptotic behavior of solutions to the linearized compressible Navier-Stokes equation around a given constant state is considered in an infinite layer Rn-1 x (0, a), n ≥ 2, under the no slip boundary condition for the momentum. The LP decay estimates of the associated semigroup are established for all 1 ≤ p ≤ ∞. It is also shown that the time-asymptotic leading part of the semigroup is given by an n -1 dimensional heat semigroup.

UR - http://www.scopus.com/inward/record.url?scp=36648999998&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36648999998&partnerID=8YFLogxK

U2 - 10.2977/prims/1201012041

DO - 10.2977/prims/1201012041

M3 - Article

AN - SCOPUS:36648999998

VL - 43

SP - 763

EP - 794

JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

SN - 0034-5318

IS - 3

ER -