  The hydrodynamics of a lattice Bose gas in a time-dependent external
potential is studied in a mean-field approximation. The conditions under which
a Mott insulating region can melt, and the local density adjust to the new
potential, are determined. In the case of a suddenly switched potential, it is
found that the Mott insulator stays insulating and the density will not adjust
if the switch is too abrupt. This comes about because too rapid currents result
in Bloch oscillation-type current reversals. For a stirrer moved through a Mott
insulating cloud, it is seen that only if the stirrer starts in a superfluid
region and the velocity is comparable to the time scale set by the tunneling,
will the Mott insulator be affected.
