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Volume 27, Issue 4
A Nine-Modes Truncation of the Plane Incompressible Navier-Stokes Equations

Heyuan Wang & Yan Cui

Commun. Math. Res., 27 (2011), pp. 297-306.

Published online: 2021-05

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  • 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.

  • Keywords

the Navier-Stokes equation, the strange attractor, Lyapunov function, bifurcation, chaos.

  • AMS Subject Headings

76D05, 58F13

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-297, author = {Wang , Heyuan and Cui , Yan}, title = {A Nine-Modes Truncation of the Plane Incompressible Navier-Stokes Equations}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {4}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19073.html} }
TY - JOUR T1 - A Nine-Modes Truncation of the Plane Incompressible Navier-Stokes Equations AU - Wang , Heyuan AU - Cui , Yan JO - Communications in Mathematical Research VL - 4 SP - 297 EP - 306 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19073.html KW - the Navier-Stokes equation, the strange attractor, Lyapunov function, bifurcation, chaos. AB -

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.

Heyuan Wang & Yan Cui. (2021). A Nine-Modes Truncation of the Plane Incompressible Navier-Stokes Equations. Communications in Mathematical Research . 27 (4). 297-306. doi:
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