  We show that the system of equations describing a magnetoviscoelastic fluid
in three dimensions can be cast as a quasilinear parabolic system. Using the
theory of maximal $L_p$-regularity, we establish existence and uniqueness of
local strong solutions and we show that each solution is smooth (in fact
analytic) in space and time. Moreover, we give a complete characterization of
the set of equilibria and show that solutions that start out close to a
constant equilibrium exist globally and converge to a (possibly different)
constant equilibrium. Finally, we show that every solution that is eventually
bounded in the topology of the state space exists globally and converges to the
set of equilibria.
