Ergodicity of Burgers' system

We consider a stochastic version of a system of coupled two equa tions formulated by Burgers [2] with the aim to describe the laminar and turbulent motions of a fluid in a channel. The existence and uniqueness of the solution as well as the irreducibility property of such system were given by Twardowska and Zabczyk [18, 19, 20]. In the paper the existence of a unique invariant measure is investigated. The paper generalizes the results of Da Prato, Debussche and Temam [4], and Da Prato and Gatarek [5], dealing with one equation describing the turbulent motion only