ON THE STRUCTURE OF THE BBGKY HIERARCHY FOR A BOLTZMANN GAS,

The authors treat the evolution in time of a spatially uniform Boltzmann gas with no initial correlations. For the case of cut-off potentials and arbitrary initial velocity distribution functions, on using the expansion parameter nr sub o to the 3rd power, with n particle density and r sub o range of binary potential, they show for terms of the order nr sub o to the 3rd power squared and lower that the hierarchy is formally self-closing even with the inclusion of many body effects i.e., at a given order in nr sub o to the 3rd power, with the exception of contributions linear in the single particle distribution function of the same order, the binary correlation function which determines the kinetic behavior of the single-particle distribution function only depends on functions which are themselves fully determinable within a prescribed iteration procedure. The actual convergence of the various orders of the formal expansion is discussed for initially aribtrary velocity distributions and for linearizations around Maxwellian velocity distributions. Author