Measure attractor for a stochastic Klein-Gordon-Schrödinger type system

Abstract

In this paper, we study the long time behavior in the distribution sense of solutions for a stochastic Klein-Gordon-Schrödinger type system, which is defined in a unbounded domain. The existence of one stationary measure from any moment-finite initial data in the space $H^{1}(\mathbb{R})\times H^{1}(\mathbb{R})\times L^{2}(\mathbb{R})$ is proven and then a global measure attractor is constructed consisting of probability measures supported on $H^{2}(\mathbb{R})\times H^{2}(\mathbb{R})\times H^{1}(\mathbb{R}). $