On the Evolution Operator of the Gradient Diffusion Hierarchy for Plane Rotators

  • W. I. Skrypnik

Abstract

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.
Published
25.12.2001
How to Cite
SkrypnikW. I. “On the Evolution Operator of the Gradient Diffusion Hierarchy for Plane Rotators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 12, Dec. 2001, pp. 1664-85, https://umj.imath.kiev.ua/index.php/umj/article/view/4386.
Section
Research articles