Stabilization of 2D Navier–Stokes Equations by Means of Actuators with Locally Supported Vorticity

Exponential stabilization to time-dependent trajectories for the incompressible Navier–Stokes equations is achieved with explicit feedback controls. The fluid is contained in a given two-dimensional spatial domain. An appropriate finite number of actuators is constructed and the control force is, at each time instant, a linear combination of such actuators. Each actuator has its vorticity supported in a small subdomain. The velocity field is subject to Lions boundary conditions. Simulations are presented showing the stabilizing performance of the proposed feedback. The results also apply to a class of observer design problems.