The Dynamical Behavior and the Numerical Simulation of a Seven-Modes System of the Navier-Stokes Equations for a Two-Dimensional Incompressible Fluid on a Torus

Abstract

A seven-mode truncation system of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is considered. Its stationary solutions and stability are presented, the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations, is simulated numerically by computer with the changing of Reynolds number.