ABSTRACT

This work deals with the mathematical study of a system of partial differential equations related to a magnetohydrodynamic (MHD) problem. The MHD equations we consider govern the behaviour of an homogeneous incompressible conducting viscous fluid subjected to a Lorentz force due to the presence of a magnetic field. More precisely, we study a coupling between the transient Navier-Stokes equations and the stationary Maxwell equations. This model can be considered for example in industrial situations when the magnetic phenomena are known to reach their steady state “infinitely” faster than the hydrodynamics phenomena.