  We develop an exactly solvable classical kinetic model of transport in Dirac
materials accounting for strong electron-electron (e-e) and electron-hole (e-h)
collisions. We use this model to track the evolution of graphene conductivity
and properties of its collective excitations across the
hydrodynamic-to-ballistic crossover. We find the relaxation rate of electric
current by e-e collisions that is possible due to the lack of Galilean
invariance, and introduce a universal numerical measure of this non-invariance
in arbitrary dimension. We find the two branches of collective excitations in
the Dirac fluid: plasmons and electron-hole sound. The sound waves have small
viscous damping at the neutrality point both in the hydrodynamic and ballistic
regimes, but acquire large damping due to e-h friction even at slight doping.
On the contrary, plasmons acquire strong frictional damping at the neutrality
point and become well-defined in doped samples.
