Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations I: Linearized Analysis at Criticality

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

Research output: Contribution to journalArticlepeer-review

Abstract

A singularly perturbed system for doubly diffusive convection equations, called the artificial compressible system, is considered on a two-dimensional infinite layer for a parameters range where the Hopf bifurcation occurs in the corresponding incompressible system. The spectrum of the linearized operator in a time periodic function space is investigated in detail near the bifurcation point when the singular perturbation parameter is small. The results of this paper are the basis of the study of the nonlinear Hopf bifurcation problem and the singular limit of the time periodic bifurcating solutions.

Original languageEnglish
Article number60
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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