  We revise the theory of superfluid turbulence near the absolute zero of
temperature and suggest a model with differential approximation for the energy
fluxes in the k-space carried by the collective hydrodynamic motions of
quantized vortex lines and by their individual uncorrelated motions known as
Kelvin waves. The model predicts energy spectra of the hydrodynamic and the
Kelvin waves components of the system, which experience a smooth crossover
between different regimes of motion over a finite range of scales.
