### Abstract

Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a given constant state is investigated on a cylindrical domain in R ^{3}, under the no slip boundary condition for the velocity field. The L^{2} decay estimate is established for the perturbation from the constant state. It is also shown that the time-asymptotic leading part of the perturbation is given by a function satisfying a 1 dimensional heat equation. The proof is based on an energy method and asymptotic analysis for the associated linearized semigroup.

Original language | English |
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Pages (from-to) | 987-1026 |

Number of pages | 40 |

Journal | Osaka Journal of Mathematics |

Volume | 45 |

Issue number | 4 |

Publication status | Published - Dec 2008 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Osaka Journal of Mathematics*,

*45*(4), 987-1026.

**Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain.** / Kagei, Yoshiyuki; Nukumizu, Takumi.

Research output: Contribution to journal › Article

*Osaka Journal of Mathematics*, vol. 45, no. 4, pp. 987-1026.

}

TY - JOUR

T1 - Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain

AU - Kagei, Yoshiyuki

AU - Nukumizu, Takumi

PY - 2008/12

Y1 - 2008/12

N2 - Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a given constant state is investigated on a cylindrical domain in R 3, under the no slip boundary condition for the velocity field. The L2 decay estimate is established for the perturbation from the constant state. It is also shown that the time-asymptotic leading part of the perturbation is given by a function satisfying a 1 dimensional heat equation. The proof is based on an energy method and asymptotic analysis for the associated linearized semigroup.

AB - Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a given constant state is investigated on a cylindrical domain in R 3, under the no slip boundary condition for the velocity field. The L2 decay estimate is established for the perturbation from the constant state. It is also shown that the time-asymptotic leading part of the perturbation is given by a function satisfying a 1 dimensional heat equation. The proof is based on an energy method and asymptotic analysis for the associated linearized semigroup.

UR - http://www.scopus.com/inward/record.url?scp=57049175816&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57049175816&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:57049175816

VL - 45

SP - 987

EP - 1026

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 4

ER -