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We show the continuity of a specific cost functional $J(\phi) = \mathbb{E}\sup_{ t \in [0,T]}(\varphi(\mathcal{L}[t,u_\phi(t), \phi(t)]))$ of the SNSE in2D on an open bounded nonperiodic domain $\mathcal{O}$ with respect to aspecial set of feedback controls $\{\phi_n\}_{n \geq 0}$, where $\varphi(x)=\log(1 + x)^{1-\epsilon}$ with $0 < \epsilon <1$.

Continuity of Cost Functional and Optimal FeedbackControls for the Stochastic Navier Stokes Equation in2D