  The present work is devoted to the study of dynamical features of Bohmian
measures, recently introduced by the authors. We rigorously prove that for
sufficiently smooth wave functions the corresponding Bohmian measure furnishes
a distributional solution of a nonlinear Vlasov-type equation. Moreover, we
study the associated defect measures appearing in the classical limit. In one
space dimension, this yields a new connection between mono- kinetic Wigner and
Bohmian measures. In addition, we shall study the dynamics of Bohmian measures
associated to so-called semi-classical wave packets. For these type of wave
functions, we prove local in-measure convergence of a rescaled sequence of
Bohmian trajectories towards the classical Hamiltonian flow on phase space.
Finally, we construct an example of wave functions whose limiting Bohmian
measure is not mono-kinetic but nevertheless equals the associated Wigner
measure.
