Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations II: Bifurcation and Stability

Chun Hsiung Hsia, Yoshiyuki Kagei, Takaaki Nishida, Yuka Teramoto

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    1 Citation (Scopus)

    Abstract

    A singular perturbation problem from the artificial compressible system to the incompressible system is considered for a doubly diffusive convection when a Hopf bifurcation from the motionless state occurs in the incompressible system. It is proved that the Hopf bifurcation also occurs in the artificial compressible system for small singular perturbation parameter, called the artificial Mach number. The time periodic solution branch of the artificial compressible system is shown to converge to the corresponding bifurcating branch of the incompressible system in the singular limit of vanishing artificial Mach number.

    Original languageEnglish
    Article number59
    JournalJournal of Mathematical Fluid Mechanics
    Volume23
    Issue number3
    DOIs
    Publication statusPublished - Aug 2021

    ASJC Scopus subject areas

    • Mathematical Physics
    • Condensed Matter Physics
    • Computational Mathematics
    • Applied Mathematics

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