  We address the effect of classical noise on the dynamics of quantum
correlations, entanglement and quantum discord, of two non-interacting qubits
initially prepared in a Bell state. The effect of noise is modeled by
randomizing the single-qubit transition amplitudes. We address both static and
dynamic environmental noise corresponding to interaction with separate common
baths in either Markovian and non-Markovian regimes. In the Markov regime, a
monotone decay of the quantum correlations is found, whereas for non-Markovian
noise sudden death and revival phenomena may occur, depending on the
characteristics of the noise. Entanglement and quantum discord show the same
qualitative behavior for all kind of noises considered. On the other hand, we
find that separate and common environments may play opposite roles in
preserving quantum correlations, depending on the noise regime considered.
