  Direct current in clean semiconductors and metals was recently shown to obey
the laws of hydrodynamics in a broad range of temperatures and sample
dimensions. However, the determination of frequency window for hydrodynamic
phenomena remains challenging. Here, we reveal a phenomenon being a hallmark of
high-frequency hydrodynamic transport, the Cerenkov emission of plasmons by
drifting Dirac electrons. The effect appears in hydrodynamic regime only due to
reduction of plasmon velocity by electron-electron collisions below the
velocity of carrier drift. To characterize the Cerenkov effect quantitatively,
we analytically find the high-frequency non-local conductivity of drifting
Dirac electrons across the hydrodynamic-to-ballistic crossover. We find the
growth rates of hydrodynamic plasmon instabilities in two experimentally
relevant setups: parallel graphene layers and graphene covered by subwavelength
grating, further showing their absence in ballistic regime. We argue that the
possibility of Cerenkov emission is linked to singular structure of non-local
conductivity of Dirac materials and is independent on specific dielectric
environment.
