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March/April 2016 Spectral properties of the semigroup for the linearized compressible Navier-Stokes equation around a parallel flow in a cylindrical domain
Reika Aoyama, Yoshiyuki Kagei
Adv. Differential Equations 21(3/4): 265-300 (March/April 2016).

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.

Citation

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Reika Aoyama. Yoshiyuki Kagei. "Spectral properties of the semigroup for the linearized compressible Navier-Stokes equation around a parallel flow in a cylindrical domain." Adv. Differential Equations 21 (3/4) 265 - 300, March/April 2016.

Information

Published: March/April 2016
First available in Project Euclid: 18 February 2016

zbMATH: 1382.35204
MathSciNet: MR3461295

Subjects:
Primary: 35B40, 35Q35

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 3/4 • March/April 2016
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