Tohoku Mathematical Journal
2002
September
SECOND SERIES VOL. 54, NO. 3

Tohoku Math. J.
54 (2002), 329-365

Title BIFURCATION ANALYSIS OF KOLMOGOROV FLOWS

Author Mami Matsuda and Sadao Miyatake

(Received June 4, 1998, revised February 25, 2002)
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.

2000 Mathematics Subject Classification. Primary 35Q30; Secondary 76D06, 37Gxx.
Key words and phrases. Navier-Stokes equations, bifurcation, continued fractions.

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