  We consider long and narrow spin valves composed of a first magnetic layer
with a single domain wall (DW), a normal metal spacer and a second magnetic
layer that is a planar or a perpendicular polarizer. For these structures, we
study numerically DW dynamics taking into account the spin torques due to the
perpendicular spin currents. We obtain high DW velocities: 50 m/s for planar
polarizer and 640 m/s for perpendicular polarizer for J = 5*10^6 A/cm^2. These
values are much larger than those predicted and observed for DW motion due to
the in-plane spin currents. The ratio of the magnitudes of the torques, which
generate the DW motion in the respective cases, is responsible for these large
differences.
