  We investigate the dynamics of quantum entanglement and more general quantum
correlations quantified respectively via negativity and local quantum
uncertainty for two qubit systems undergoing Markovian collective dephasing.
Focusing on a two-parameter family of initial two-qubit density matrices, we
study the relation of the emergence of the curious phenomenon of time-invariant
entanglement and the dynamical behavior of local quantum uncertainty.
Developing an illustrative geometric approach, we demonstrate the existence of
distinct regions of quantum entanglement for the considered initial states and
identify the region that allows for completely frozen entanglement throughout
the dynamics, accompanied by generation of local quantum uncertainty.
Furthermore, we present a systematic analysis of different dynamical behaviors
of local quantum uncertainty such as its sudden change or smooth amplification,
in relation with the dynamics of entanglement.
