  The entanglement evolution of two qubits under local, single- and two- sided
noisy channels is investigated. It is found that for all pure initial states,
the entanglement under a one-sided noisy channel is completely determined by
the maximal trace distance which is the main element to construct the measure
of non-Markovianity. For the two-sided noisy channel case, when the qubits are
initially prepared in a general class of states, no matter pure or mixed, the
entanglement can be expressed as the products of initial entanglement and the
channels' action on the maximally entangled state.
