Dynamics and control of the 2-d Navier-Stokes equations

作者：Smaoui Nejib^*; Zribi Mohamed

来源：Applied Mathematics and Computation, 2014, 237: 461-473.

DOI：10.1016/j.amc.2014.03.150

• Two-dimensional Navier-Stokes equations
• Bifurcations
• Dynamical systems and control

This paper deals with the dynamics and control of the two-dimensional (2-d) Navier-Stokes (N-S) equations with a spatially periodic and temporally steady forcing term. First, we construct a dynamical system of nine nonlinear differential equations by Fourier expansion and truncation of the 2-d N-S equations. Then, we study the dynamics of the obtained reduced order system by analyzing the system's attractors for different values of the Reynolds number, R-e. By applying the symmetry of the equations on one of the system's attractors, a symmetric limit trajectory that is part of the dynamics is obtained. Moreover, a Lyapunov based control strategy to control the dynamics of the system for a given R-e is designed. Finally, numerical simulations are undertaken to validate the theoretical developments.

• 出版日期2014-6-15