TY - JOUR
AU - W. I. Skrypnik
PY - 2001/12/25
Y2 - 2024/10/07
TI - On the Evolution Operator of the Gradient Diffusion Hierarchy for Plane Rotators
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 53
IS - 12
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/4386
AB - By using a high-temperature cluster expansion, we construct the evolution operator of the BBGKY-type gradient diffusion hierarchy for plane rotators that interact via a summable pair potential in a Banach space containing the Gibbs (stationary) correlation functions. We prove the convergence of this expansion for a sufficiently small time interval. As a result, we prove that weak solutions of the hierarchy exist in the same Banach space. If the initial correlation functions are locally perturbed Gibbs correlation functions, then these solutions are defined on an arbitrary time interval.
ER -