On the spectrum for the artificial compressible system

Yoshiyuki Kagei, Takaaki Nishida, Yuka Teramoto

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Stability of stationary solutions of the incompressible Navier–Stokes system and the corresponding artificial compressible system is considered. Both systems have the same sets of stationary solutions and the incompressible system is obtained from the artificial compressible one in the zero limit of the artificial Mach number ϵ which is a singular limit. It is proved that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion by variational method with admissible functions being only potential flow parts of velocity fields, then it is also stable as a solution of the artificial compressible one for sufficiently small ϵ. The result is applied to the Taylor problem.

Original languageEnglish
Pages (from-to)897-928
Number of pages32
JournalJournal of Differential Equations
Volume264
Issue number2
DOIs
Publication statusPublished - Jan 15 2018
Externally publishedYes

Keywords

  • Artificial compressible system
  • Incompressible Navier–Stokes system
  • Singular perturbation
  • Stability
  • Taylor vortex

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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