  We present synchronization and contractivity estimates for the kinetic
Kuramoto model obtained from the Kuramoto phase model in the mean-field limit.
For identical Kuramoto oscillators, we present an admissible class of initial
data leading to time-asymptotic complete synchronization, that is, all measure
valued solutions converge to the traveling Dirac measure concentrated on the
initial averaged phase. If two initial Radon measures have the same natural
frequency density function and strength of coupling, we show that the
Wasserstein p-distance between corresponding measure valued solutions is
exponentially decreasing in time. This contraction principle is more general
than previous L1-contraction properties of the Kuramoto phase model.
