10.2748/tmj/1113247600
1916632
110000026987
BIFURCATION ANALYSIS OF KOLMOGOROV FLOWS
en
abstract
We examine the bifurcation curves of solutions to the Kolmogorov problem and present the exact formula for the second derivatives of their components concerning Reynolds numbers at bifurcation points. Using this formula, we show the supercriticality of these curves in the case where the ratio of periodicities in two directions is close to one. In order to prove this, we construct an inverse matrix of infinite order, whose elements are given by sequences generated by continued fractions. For this purpose, we investigate some fundamental properties of these sequences such as quasi-monotonicity and exponential decay from general viewpoints.
disallow
9000021529660
MATSUDA MAMI
Department of Mathematics, Faculty of Science and Technology, Science University of Tokyo
8000000368614
9000021529664
9000350600570
9000020020569
MIYATAKE SADAO
Department of Mathematics, Faculty of Science, Nara Women's University
00408735
2186585X
TOMJAM
AA00863953
Tohoku Mathematical Journal, Second Series
Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ
Tohoku Math. J.
Tohoku math. J
東北数学雑誌
Mathematical Institute, Tohoku University
東北大学大学院理学研究科数学専攻
2002
54
3
329
365
false
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Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori
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Example of the generation of a secondary stationary or periodic flow when there is loss of stability of the laminar flow of a viscous incompressible fluid
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Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere
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An Example of Instability for the Navier–Stokes Equations on the 2–dimensional Torus
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Bifurcation from simple eigenvalues
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Stationary solutions and their stability for Kimura’s diffusion model with intergroup selection
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Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid
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Kolmogorov flow and laboratory simulation of it
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Landau Equation and Mean Flow Distortion in Nonlinear Stability Theory of Parallel Free Flows
Landau Equation and Mean Flow Distortio
Nonlinear Stability Theory of Spatially Periodic Parallel Flows
Nonlinear Stability Theory of Spatially
oai:japanlinkcenter.org:0029752534
10.2748/tmj/1113247600
110000026987
10.1007/s00021-022-00718-y_references_DOI_YVyPeggJjg4dWgzAlyjNkA8pREr