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Continuity of cost functional and optimal feedback controls for the stochastic Navier Stokes equation in 2D

  • Author Bio: E-mail address: kugurlu@usc.edu
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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 in 2D on an open bounded nonperiodic domain $\mathcal{O}$ with respect to a special set of feedback controls $\{\phi_n\}_{n \geq 0}$, where $\varphi(x) =\log(1 + x)^{1-\epsilon}$ with $0 < \epsilon < 1$.

    Mathematics Subject Classification: 60H15, 60H30.


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