Advances in Differential Equations

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

Reika Aoyama and Yoshiyuki Kagei

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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.

Article information

Source
Adv. Differential Equations Volume 21, Number 3/4 (2016), 265-300.

Dates
First available in Project Euclid: 18 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ade/1455805259

Mathematical Reviews number (MathSciNet)
MR3461295

Zentralblatt MATH identifier
06550103

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 35B40: Asymptotic behavior of solutions

Citation

Aoyama, Reika; Kagei, Yoshiyuki. Spectral properties of the semigroup for the linearized compressible Navier-Stokes equation around a parallel flow in a cylindrical domain. Adv. Differential Equations 21 (2016), no. 3/4, 265--300. https://projecteuclid.org/euclid.ade/1455805259.


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