Abstract : We study a MHD system consisting of the stationary Maxwell equations coupled with the transient Navier-Stokes equations. We prove that a solution exists and is unique for small time and small data. We show that the system may become ill-posed as soon as the fluid velocity becomes too large.
Jean-Frédéric Gerbeau, Claude Le Bris. A coupled system arising in Magnetohydrodynamics. Applied Mathematics Letters, Elsevier, 1999, 12 (3), pp.53-57. ⟨10.1016/S0893-9659(98)00172-4⟩. ⟨hal-00691693⟩