  The dynamics of a domain wall driven by a spin-polarized current in a
mesoscopic system is studied numerically. Spin-mixing in the states of the
conduction electrons is fully taken into account. When the Fermi energy of the
electrons is larger than the exchange energy ($E_{\rm F}>J_{\rm sd}$), the spin
precession induces spin wave excitations in the local spins which contribute
towards the displacement of the domain wall. The resulting average velocity is
found to be much smaller than the one obtained in the adiabatic limit. For
$E_{\rm F}<J_{\rm sd}$, the results are consistent with the adiabatic
approximation except for the region below the critical current where a residual
domain wall velocity is found.
