Stability enhancement by boundary control in 2D channel flow. I. Regularity of solutions

We stabilize the parabolic equilibrium profile in a 2D channel flow using actuators and wall-shear-stress sensors only at the wall. The control of channel flow was previously considered by Speyer et al (1999), and Bewley et al, who derived feedback laws based on linear optimal control, and implemented by wall-normal actuation. With an objective to achieve global Lyapunov stabilization, we arrive at a feedback law using tangential actuation (using teamed pairs of synthetic jets) and only local measurements, allowing to embed the feedback in MEMS hardware, without need for wiring. This feedback is shown to guarantee global stability in at least H² norm, which by Sobolev´s embedding theorem implies continuity in space and time of both the flow field and the control (as well as their convergence to the desired steady state)