  The recent demonstrations of viscous hydrodynamic electron flow in
two-dimensional electron systems poses serious questions to the validity of
existing transport theories, including the ballistic model, the
collision-induced and collisionless hydrodynamics. While the theories of
transport at hydrodynamic-to-ballistic crossover for free 2d electrons are well
established, the same is not true for electrons in magnetic fields. In this
work, we develop an analytically solvable model describing the transition from
ballistic to hydrodynamic transport with changing the strength of
electron-electron collisions in magnetic fields. Within this model, we find an
expression for the high-frequency non-local conductivity tensor of 2d
electrons. It is valid at arbitrary relation between frequency of external
field $\omega$, the cyclotron frequency $\omega_c$, and the frequency of e-e
collisions $\tau^{-1}_{ee}$. We use the obtained expression to study the
transformation of 2d magnetoplasmon modes at hydrodynamic-to-ballistic
crossover. In the true hydrodynamic regime, $\omega\tau_{ee} \ll 1$, the 2DES
supports a single magnetoplasmon mode that is not split at cyclotron harmonics.
In the ballistic regime, $\omega\tau_{ee} \gg 1$, the plasmon dispersion
develops splittings at cyclotron harmonics, forming the Bernstein modes. A
formal long-wavelength expansion of kinetic equations ("collisionless
hydrodynamics") predicts the first splitting of plasmon dispersion at
$\omega\approx 2\omega_c$. Still, such expansion fails to predict the zero and
negative group velocity sections of true magnetoplasmon dispersion, for which
the full kinetic model is required.
