Kinetic approach to the long-time behaviour in fluids. I. A formal inequality for the time-dependent collision operator

We start here an investigation of the kinetic justification to the t- 3 2 behaviour of the Green-Kubo integrands in three-dimensional fluids and of other related problems. We present an analysis of the time-dependent collision operator; this analysis is formal but involves no approximation. We derive an inequality for the various contributions to this operator, which will be used in a subsequent paper to derive the t- 3 2 behaviour. The method uses assumptions on the behaviour of the hydrodynamical propagators which will be justified in another paper. © 1973.SCOPUS: ar.j