TY - JOUR
T1 - Singular Limit in Hopf Bifurcation for Doubly Diffusive Convection Equations II
T2 - Bifurcation and Stability
AU - Hsia, Chun Hsiung
AU - Kagei, Yoshiyuki
AU - Nishida, Takaaki
AU - Teramoto, Yuka
N1 - Funding Information:
C.-H. Hsia was partly supported by NCTS and MOST Grant 109-2115-M-002-013-MY3. Y. Kagei was partly supported by JSPS KAKENHI Grant Numbers 16H03947, 16H06339 and 20H00118. T. Nishida is partly supported by JSPS KAKENHI Grant Number 20K03699.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2021/8
Y1 - 2021/8
N2 - 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.
AB - 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.
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U2 - 10.1007/s00021-021-00583-1
DO - 10.1007/s00021-021-00583-1
M3 - Article
AN - SCOPUS:85105471599
SN - 1422-6928
VL - 23
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
IS - 3
M1 - 59
ER -