The Initial Value Problem for L^∞ Data: Thermodynamic Limit

Abstract

In the previous Chapter the solutions of the initial value problem for the BBGKY hierarchy have been constructed for systems with a finite average number of particles (or zero density in the entire space ℝ^v). To describe the evolution of states of infinite systems we must construct the solutions in a functional space different from L¹, which contains the sequences of distribution functions, describing states of infinite systems. Such functional space is the space L^∞_ξ of the sequences of functions bounded with respect to the configuration variables and decreasing with respect to the momentum ones (this space was defined in Section 1.5). As is well-known, the equilibrium distribution functions belong to this space.