Stabilization of a 3-D Periodic Channel Flow by Explicit Normal Boundary Feedbacks

We design here explicit finite-dimensional boundary stabilizing feedbacks for the parabolic Poiseuille profile of an infinite 3-D channel flow. The controller acts on the normal component of the velocity, and it is easy to manipulate from the computational point of view. The stability is achieved without any a priori condition on the viscosity coefficient, that is on the Reynolds number; however, the lower the value of the viscosity is, the higher the dimension of the feedback is.