Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct

Abstract

This article is concerned with the global exact controllability for ideal incompressible magnetohydrodynamics in a rectangular domain where the controls are situated in both vertical walls. First, global exact controllability via boundary controls is established for a related Elsässer type system by applying the return method, introduced in [Coron J.M., Math. Control Signals Systems, 5(3) (1992) 295--312]. Similar results are then inferred for the original magnetohydrodynamics system with the help of a special pressure-like corrector in the induction equation. Overall, the main difficulties stem from the nonlinear coupling between the fluid velocity and the magnetic field in combination with the aim of exactly controlling the system. In order to overcome some of the obstacles, we introduce ad-hoc constructions, such as suitable initial data extensions outside of the physical part of the domain and a certain weighted space.

Analysis of factors affecting destabilization of a viscous liquid flow in channels

“…Quite often, destabilization of the flow is observed in equipment associated with the processes and apparatuses of chemical technology, in the oil refining industry and in physicochemical mechanics. The factors influencing the flow destabilization can be the physicochemical and rheological properties of liquid media, the manifestation of inertia forces from convective acceleration, heat transfer conditions, and the influence of ponderomotive forces of a magnetic nature on the flow of an electrically conductive fluid [1][2][3]. A number of works by [4][5][6] are devoted to the study of these problems.…”