Hydrodynamic theory of Brownian motion in a compressible fluid (Q2755238)

A general analytic solution of the problem of time correlations in the theory of Brownian motion is obtained taking into account the compressibility of fluid and the presence of harmonic potential. On the basis of this solution, the authors formulate criteria for the realization of diffusion regime at large time scale. A consistent limit procedure on small time scale has been performed to approach the equilibrium value of the mean square velocity. The full asymptotic expansions have been found for velocity autocorrelation functions and for the mean square displacements of a Brownian particle which describe the so-called persistent correlations in a compressible viscous fluid.