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 - <p style="text-align: justify;">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.</p>