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

Reika Aoyama, Yoshiyuki Kagei

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)265-300
Number of pages36
JournalAdvances in Differential Equations
Volume21
Issue number3-4
Publication statusPublished - Jan 1 2016

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Spectral Projection
Parallel flow
Compressible Navier-Stokes Equations
Nonlinear Stability
Spectral Properties
Heat Equation
Navier Stokes equations
Nonlinear Problem
Semigroup
Infinity
Decay
Operator
Estimate
Mach number
Reynolds number
Hot Temperature

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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

In: Advances in Differential Equations, Vol. 21, No. 3-4, 01.01.2016, p. 265-300.

Research output: Contribution to journalArticle

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