Mathematical study of a coupled system arising in magnetohydrodynamics (Q2708578)

The paper deals with a mathematical model for a homogeneous incompressible conducting viscous fluid subjected to a Lorentz force due to the presence of a magnetic field, i.e. with a coupled system of transient Navier-Stokes equations and of stationary elliptic Maxwell equations. Under some reasonable assumptions upon the physical data, the authors prove the existence and the uniqueness of the strong solution on a time interval whose length depends on the data. If the velocity becomes too large, the above system may become ill-posed which implies a greater care in numerical simulations.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00037].