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

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

Research output: Contribution to journalArticlepeer-review

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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