### Abstract

Large time behavior of solutions to the compressible Navier-Stokes equation around a given constant state is considered in an infinite layer R^{n-1} ×(0,a)n ≥ 2, under the no slip boundary condition for the velocity. The L^{p} decay estimates of the solution are established for all 1≤ p≤∞. It is also shown that the time-asymptotic leading part of the solution is given by a function satisfying the n - 1 dimensional heat equation. The proof is given by combining a weighted energy method with time-weight functions and the decay estimates for the associated linearized semigroup.

Original language | English |
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Pages (from-to) | 95-124 |

Number of pages | 30 |

Journal | Hiroshima Mathematical Journal |

Volume | 38 |

Issue number | 1 |

Publication status | Published - Mar 2008 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

*Hiroshima Mathematical Journal*,

*38*(1), 95-124.

**Large time behavior of solutions to the compressible Navier-stokes equation in an infinite layer.** / Kagei, Yoshiyuki.

Research output: Contribution to journal › Article

*Hiroshima Mathematical Journal*, vol. 38, no. 1, pp. 95-124.

}

TY - JOUR

T1 - Large time behavior of solutions to the compressible Navier-stokes equation in an infinite layer

AU - Kagei, Yoshiyuki

PY - 2008/3

Y1 - 2008/3

N2 - Large time behavior of solutions to the compressible Navier-Stokes equation around a given constant state is considered in an infinite layer Rn-1 ×(0,a)n ≥ 2, under the no slip boundary condition for the velocity. The Lp decay estimates of the solution are established for all 1≤ p≤∞. It is also shown that the time-asymptotic leading part of the solution is given by a function satisfying the n - 1 dimensional heat equation. The proof is given by combining a weighted energy method with time-weight functions and the decay estimates for the associated linearized semigroup.

AB - Large time behavior of solutions to the compressible Navier-Stokes equation around a given constant state is considered in an infinite layer Rn-1 ×(0,a)n ≥ 2, under the no slip boundary condition for the velocity. The Lp decay estimates of the solution are established for all 1≤ p≤∞. It is also shown that the time-asymptotic leading part of the solution is given by a function satisfying the n - 1 dimensional heat equation. The proof is given by combining a weighted energy method with time-weight functions and the decay estimates for the associated linearized semigroup.

UR - http://www.scopus.com/inward/record.url?scp=57049180051&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57049180051&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:57049180051

VL - 38

SP - 95

EP - 124

JO - Hiroshima Mathematical Journal

JF - Hiroshima Mathematical Journal

SN - 0018-2079

IS - 1

ER -