Dynamics and control of the seven-mode truncation system of the 2-d Navier-Stokes equations

摘要

This paper deals with the dynamics and control problem of the two dimensional Navier-Stokes equations. A seventh order system of nonlinear ordinary differential equations which approximates the behavior of the Navier-Stokes equations is obtained by using the Fourier Galerkin method. Extensive simulations show that the obtained system is able to display the different behaviors of the Navier-Stokes equations. Then the paper proposes two Lyapunov based controllers to either control the system of ordinary differential equations to a desired fixed point or to synchronize two ordinary differential equations systems obtained from the two dimensional Navier-Stokes equations under different initial conditions. The proposed control schemes are simulated using the MATLAB software and the simulation results show their effectiveness. (C) 2015 Elsevier B.V. All rights reserved.