Boundary stabilization of a 2-D periodic MHD channel flow, by proportional feedbacks

Alexandru Ioan Cuza University, Department of Mathematics, and Octav Mayer Institute of Mathematics (Romanian Academy), Bvd. Carol I no. 11, 700506 Iaşi, Romania.
ionut.munteanu@uaic.ro

Received: 17 December 2015
Revised: 19 April 2016

Abstract

We consider an electrically conducting 2-D channel fluid flow affected by a transverse magnetic field. The governing equations are the magnetohydrodynamics equations. We design an explicit finite-dimensional exponentially stabilizing feedback, given in a very simple form, easily manageable from the computational point of view, for the Hartmann−Poiseuille profile. Moreover, the stability is assured independently of the value of the magnetic Reynolds number. The control acts on the normal components of both velocity and magnetic field, on the upper wall only.