  Gaia DR2 has delivered full-sky 6-D measurements for millions of stars, and
the quest to understand the dynamics of our Galaxy has entered a new phase. Our
aim is to reveal and characterize the kinematic sub-structure of the different
Galactic neighbourhoods, to form a picture of their spatial evolution that can
be used to infer the Galactic potential, its evolution and its components. We
take ~5 million stars in the Galactic disk from the Gaia DR2 catalogue and
build the velocity distribution of many different Galactic Neighbourhoods
distributed along 5 kpc in Galactic radius and azimuth. We decompose their
distribution of stars in the V_R-V_phi plane with the wavelet transformation
and asses the statistical significance of the structures found. We detect many
kinematic sub-structures (arches and more rounded groups) that diminish their
azimuthal velocity as a function of Galactic radius in a continuous way,
connecting volumes up to 3 kpc apart in some cases. The decrease rate is, on
average, of ~23 km/s/kpc. In azimuth, the kinematic sub-structures present much
smaller variations. We also observe a duality in their behaviour: some conserve
their vertical angular momentum with radius (e.g., Hercules), while some seem
to have nearly constant kinetic energy (e.g., Sirius). These two trends are
consistent with the approximate predictions of resonances and of phase mixing,
respectively. Besides, the overall spatial evolution of Hercules is consistent
with being related to the Outer Lindblad Resonance of the Bar. We also detect
structures without apparent counterpart in the vicinity of the Sun. The various
trends observed and their continuity with radius and azimuth allows for future
work to deeply explore the parameter space of the models. Also, the
characterization of extrasolar moving groups opens the opportunity to expand
our understanding of the Galaxy beyond the Solar Neighbourhood.
