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Gaia DR2 has delivered full-sky 6-D measurements for millions of stars, andthe quest to understand the dynamics of our Galaxy has entered a new phase. Ouraim is to reveal and characterize the kinematic sub-structure of the differentGalactic neighbourhoods, to form a picture of their spatial evolution that canbe used to infer the Galactic potential, its evolution and its components. Wetake ~5 million stars in the Galactic disk from the Gaia DR2 catalogue andbuild the velocity distribution of many different Galactic Neighbourhoodsdistributed along 5 kpc in Galactic radius and azimuth. We decompose theirdistribution of stars in the V_R-V_phi plane with the wavelet transformationand asses the statistical significance of the structures found. We detect manykinematic sub-structures (arches and more rounded groups) that diminish theirazimuthal 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, onaverage, of ~23 km/s/kpc. In azimuth, the kinematic sub-structures present muchsmaller variations. We also observe a duality in their behaviour: some conservetheir vertical angular momentum with radius (e.g., Hercules), while some seemto have nearly constant kinetic energy (e.g., Sirius). These two trends areconsistent with the approximate predictions of resonances and of phase mixing,respectively. Besides, the overall spatial evolution of Hercules is consistentwith being related to the Outer Lindblad Resonance of the Bar. We also detectstructures without apparent counterpart in the vicinity of the Sun. The varioustrends observed and their continuity with radius and azimuth allows for futurework to deeply explore the parameter space of the models. Also, thecharacterization of extrasolar moving groups opens the opportunity to expandour understanding of the Galaxy beyond the Solar Neighbourhood.

Riding the kinematic waves in the Milky Way disk with Gaia