  We study the global well-posedness of magnetohydrodynamic (MHD) equations.
The hydrodynamic system consists of the Navier-Stokes equations for the fluid
velocity coupled with a reduced from of the Maxwell equations for the magnetic
field. The fluid velocity is assumed to satisfy a no-slip boundary condition,
while the magnetic field is subject to a time-dependent Dirichlet boundary
condition. We first establish the global existence of weak and strong solutions
to (1.1)-(1.4). Then we derive the existence of a uniform attractor for
(1.1)-(1.4).
