Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv,

Ukraine

E-mail: vyrtum@imath.kiev.ua

**On regularized expansions for the BBGKY hierarchy solutions**

**Abstract:**

We construct the regularized expansion for a cumulant (semi-invariant)
representation for the solution of the initial value problem for the BBGKY
hierarchy of equations. We prove that there are no divergent integrals
in every term of such regularized expansion. For the one-dimensional infinite
particle system interacting via a short-range potential the local in time
existence theorem is proved.