Year: 2011
Author: Heyuan Wang, Yan Cui
Communications in Mathematical Research , Vol. 27 (2011), Iss. 4 : pp. 297–306
Abstract
In this paper a nine-modes truncation of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained. The stationary solutions, the existence of attractor and the global stability of the equations are firmly proved. What is more, that the force $f$ acts on the mode $k_3$ and $k_7$ respectively produces two systems, which lead to a much richer and varied phenomenon. Numerical simulation is given at last, which shows a stochastic behavior approached through an involved sequence of bifurcations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-CMR-19073
Communications in Mathematical Research , Vol. 27 (2011), Iss. 4 : pp. 297–306
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: the Navier-Stokes equation the strange attractor Lyapunov function bifurcation chaos.