Evolution operator of the Bogolyubov gradient diffusion hierarchy in the mean field limit

The evolution operator and weak solutions are constructed on a finite time interval in the space of sequences of measurable bounded functions for the bogolyubov gradient diffusion hierarchy in the mean field limit. The author considers an infinite system of diffusing particles that interact through a two-body potential var-epsilon, Φ, var-epsilon > 0, and have density proportional to var-epsilon -1