On the spectrum for the artificial compressible system

Yoshiyuki Kagei, Takaaki Nishida, Yuka Teramoto

    Research output: Contribution to journalArticlepeer-review

    7 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

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Applied Mathematics

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