Boundary Feedback Stabilization of Periodic Fluid Flows in a Magnetohydrodynamic Channel

摘要

In this technical note, an electrically conducting 2-D channel fluid flow, in the presence of a transverse magnetic field, is investigated. The governing equations are the magnetohydrodynamics equations, which are a coupling between the Navier-Stokes and Maxwell equations. The stability of the Hartmann-Poiseuille profile is achieved by finite-dimensional feedback controllers acting on both normal components of the velocity field and of the magnetic field, on the upper wall only.