Existence of statistical solutions of a stochastic Karman system in a bounded region

Abstract

The existence of a statistical solution to the stochastic Karman system of equations is proved without imposing constraints on the growth of the initial probability measure. Estimates of the moments of the solution are obtained, and the phase space is defined more precisely. The existence of a solution of the Cauchy problem for the corresponding Kolmogorov equation is given under the assumption that the initial mean energy is finite.