Asymptotic behavior of stochastic PDEs with random coefficients (Q977954)

The authors study stochastic partial differential equations of the form \[ \begin{cases} dX = (AX + b(X) + g(X,\overline{Y})dt + \sigma(X,\overline{Y})) dW (t), \\ X(s) = x \in H, \quad s \leq t, \end{cases} \] where \(W\) and \(\overline{Y}\) are stochatic processes. This paper generalises some results from [\textit{G. Da Prato} and \textit{A. Debussche}, J. Dyn. Differ. Equations 20, No. 2, 301--335 (2008; Zbl 1154.35099)]. The obtained results are then applied to two dimenional stochastic Navier--Stokes equations.