Advances in Differential Equations

Stability and instability of generalized Kolmogorov flows on the two-dimensional sphere

A. A. Ilyin

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Abstract

The Navier--Stokes equations on the two-dimensional rotating sphere with a family of forcing terms, whose stream functions are the Legendre polynomials $P_s$, are considered. The stability and instability properties of the corresponding generalized Kolmogorov flows are studied both analytically and numerically. Logarithmically sharp lower bounds for the dimension of the global attractor are obtained. The effect of rotation on the stability properties of the Kolmogorov flows is discussed.

Article information

Source
Adv. Differential Equations Volume 9, Number 9-10 (2004), 979-1008.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867911

Mathematical Reviews number (MathSciNet)
MR2098063

Zentralblatt MATH identifier
1099.37059

Subjects
Primary: 37L30: Attractors and their dimensions, Lyapunov exponents
Secondary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30] 76E20: Stability and instability of geophysical and astrophysical flows 76U05: Rotating fluids 86A10: Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]

Citation

Ilyin, A. A. Stability and instability of generalized Kolmogorov flows on the two-dimensional sphere. Adv. Differential Equations 9 (2004), no. 9-10, 979--1008. https://projecteuclid.org/euclid.ade/1355867911.


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