BACKSTEPPING BOUNDARY CONTROL OF MAGNETOHYDRODYNAMIC CHANNEL FLOW

We present a PDE boundary controller that stabilizes the velocity, pressure, and electromagnetic fields in a magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow, a benchmark model for applications such as cooling systems, hypersonic flight and propulsion. The system is described by the inductionless MHD equations, a combination of the Navier-Stokes equations and a Poisson equation for the electric potential under the so-called MHD approximation in a low magnetic Reynolds number regime, and is unstable for large Reynolds numbers. Our design is based on the backstepping method for parabolic systems and needs actuation of velocity and the electric potential at only one of the walls. Stabilization of non-discretized 3-D MHD channel flow has so far been an open problem.