On Regularized Solution for BBGKY Hierarchy of One-Dimensional Infinite System

TL;DR

This paper develops a regularized cumulant representation for solutions of the BBGKY hierarchy in a one-dimensional infinite hard sphere system, proving existence for bounded initial data.

Contribution

It introduces a novel regularized cumulant approach for the BBGKY hierarchy and establishes an existence theorem for solutions with bounded initial data.

Findings

Constructed a regularized cumulant representation for the BBGKY hierarchy.

Proved an existence theorem for solutions with initial data in bounded function space.

Provided a new analytical framework for infinite one-dimensional hard sphere systems.

Abstract

We construct a regularized cumulant (semi-invariant) representation of a solution of the initial value problem for the BBGKY hierarchy for a one-dimensional infinite system of hard spheres interacting via a short-range potential. An existence theorem is proved for the initial data from the space of sequences of bounded functions.