In this paper, we investigate the stochastic Cahn–Hilliard–Navier–Stokes equations in two-dimensional spaces. Applying Maslowski–Seidler method, establish existence of invariant measure state space [Formula: see text] with weak topology. We also prove global pathwise solutions using compactness argument.

A general construction for ?nite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of f n () will imply the existence of a ?nite invariant measure for the map f which is absolutely continuous with respect to , a measure on the phase space describing the sets of measure zero. Furthermore we will discuss ...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of such automata converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. Therefore we also show that for an...