  The usual derivative expansion of gravity duals of charged fluid dynamics is
known to break down in the zero temperature limit. In this case, the
fluid-gravity duality is not understood precisely. We explore this problem for
a zero temperature charged fluid driven by a low frequency, small amplitude and
spatially homogeneous external force. In the gravity dual, this corresponds to
time dependent boundary value of the dilaton. We calculate the bulk solution
for the dilaton and the leading backreaction to the metric and the gauge fields
using the modified low frequency expansion of [11]. The resulting solutions are
regular everywhere, establishing fluid-gravity duality to this order.
