Continuity of Cost Functional and Optimal FeedbackControls for the Stochastic Navier Stokes Equation in2D
We show the continuity of a specific cost functional $J(ϕ) = \mathbb{E} \sup_{ t \in [0,T]}(φ(\mathcal{L}[t,u_ϕ(t), ϕ(t)]))$ of the SNSE in 2D on an open bounded nonperiodic domain $\mathcal{O}$ with respect to a special set of feedback controls $\{ϕ_n\}_{n \geq 0}$, where $φ(x) =\log(1 + x)^{1-ε}$ with $0 < ε<1$.
math.PR↗