  We propose a covariant holographic entanglement negativity constructionfor
time-dependent mixed states of adjacent intervals in $(1+1)$-dimensional
conformal field theories dual to non-static bulk $\mathrm{AdS_3}$
configurations. Our construction applied to $(1+1)$-dimensional conformal field
theories with a conserved charge dual to non-extremal and extremal rotating BTZ
black holes exactly reproduces the corresponding replica technique results, in
the large central charge limit. We also utilize our conjecture to obtain the
time-dependent holographic entanglement negativity for the mixed state in
question for the $(1+1)$- dimensional CFT dual to a bulk
Vaidya-$\mathrm{AdS_3}$ configuration.
