  We investigate the time evolution of negativity and quantum discord for a
pair of non-interacting qubits with one being weakly coupled to a decohering
Davies--type Markovian environment. At initial time of preparation, the qubits
are prepared in one of the maximally entangled pure Bell states. In the
limiting case of pure decoherence (i.e. pure dephasing), both, the quantum
discord and negativity decay to zero in the long time limit. In presence of a
manifest dissipative dynamics, the entanglement negativity undergoes a sudden
death at finite time while the quantum discord relaxes continuously to zero
with increasing time. We find that in dephasing environments the decay of the
negativity is more propitious with increasing time; in contrast, the evolving
decay of the quantum discord proceeds weaker for dissipative environments.
Particularly, the slowest decay of the quantum discord emerges when the energy
relaxation time matches the dephasing time.
