### Abstract

This paper is concerned with the stability of a parallel flow of the compressible Navier-Stokes equation in a cylindrical domain. The spectrum of the linearized operator is analyzed for the purpose of the study of the nonlinear stability. 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 a one dimensional heat equation as time goes to infinity and the other one decays exponentially. Some estimates related to the spectral projections are established, which will also be useful for the study of the nonlinear problem.

Original language | English |
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Pages (from-to) | 265-300 |

Number of pages | 36 |

Journal | Advances in Differential Equations |

Volume | 21 |

Issue number | 3-4 |

Publication status | Published - Jan 1 2016 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Advances in Differential Equations*,

*21*(3-4), 265-300.

**Spectral properties of the semigroup for the linearized compressible Navier-Stokes equation around a parallel flow in a cylindrical domain.** / Aoyama, Reika; Kagei, Yoshiyuki.

Research output: Contribution to journal › Article

*Advances in Differential Equations*, vol. 21, no. 3-4, pp. 265-300.

}

TY - JOUR

T1 - Spectral properties of the semigroup for the linearized compressible Navier-Stokes equation around a parallel flow in a cylindrical domain

AU - Aoyama, Reika

AU - Kagei, Yoshiyuki

PY - 2016/1/1

Y1 - 2016/1/1

N2 - This paper is concerned with the stability of a parallel flow of the compressible Navier-Stokes equation in a cylindrical domain. The spectrum of the linearized operator is analyzed for the purpose of the study of the nonlinear stability. 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 a one dimensional heat equation as time goes to infinity and the other one decays exponentially. Some estimates related to the spectral projections are established, which will also be useful for the study of the nonlinear problem.

AB - This paper is concerned with the stability of a parallel flow of the compressible Navier-Stokes equation in a cylindrical domain. The spectrum of the linearized operator is analyzed for the purpose of the study of the nonlinear stability. 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 a one dimensional heat equation as time goes to infinity and the other one decays exponentially. Some estimates related to the spectral projections are established, which will also be useful for the study of the nonlinear problem.

UR - http://www.scopus.com/inward/record.url?scp=84971577958&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84971577958&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84971577958

VL - 21

SP - 265

EP - 300

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 3-4

ER -