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A simple ansatz for the study of velocity autocorrelation functions in fluidsat different timescales is proposed. The ansatz is based on an effectivesummation of the infinite continued fraction at a reasonable assumption aboutconvergence of relaxation times of the higher order memory functions, whichhave a purely kinetic origin. The VAFs obtained within our approach arecompared with the results of the Markovian approximation for memory kernels. Itis shown that although in the "overdamped" regime both approaches agree to alarge extent at the initial and intermediate times of the system evolution, ourformalism yields power law relaxation of the VAFs which is not observed at thedescription with a finite number of the collective modes. Explicit expressionsfor the transition times from kinetic to hydrodynamic regimes are obtained fromthe analysis of the singularities of spectral functions in the complexfrequency plane.

A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales