Backstepping boundary control of Navier-Stokes channel flow: a 3D extension

We present an extension from 2D to 3D of a boundary control law which stabilizes the parabolic profile of an infinite channel flow. In this 3D case, we include an additional controller in the spanwise direction which, similar to the streamwise and wall normal velocity controllers, actuates solely along one boundary. The controller that acts in the wall normal direction transforms the system into a strict feedback form. The streamwise and spanwise controllers decouple the normal vorticity from the normal velocity and then stabilize the normal velocity. This result guarantees exponential stability in the L2 sense of the linearized Navier-Stokes equations