  We study the perturbative corrections to the {
Gorini-Kossakowski-Sudarshan-Lindblad equation which arises in the weak
coupling limit}. The spin-boson model in the rotating wave approximation at
zero temperature is considered. We show that the perturbative part of the
density matrix satisfies the time-independent
Gorini-Kossakowski-Sudarshan-Lindblad equation for arbitrary order of the
perturbation theory (if all the moments of the reservoir correlation function
are finite). But to reproduce the right asymptotic precision at long times, one
should use { an initial condition different} from the one for exact dynamics.
Moreover, we show that the initial condition for this master equation even
fails to be a density matrix under certain resonance conditions.
