# American Institute of Mathematical Sciences

January  2017, 16(1): 189-208. doi: 10.3934/cpaa.2017009

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

 Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA

Received  March 2016 Revised  July 2016 Published  November 2016

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 $0 < \epsilon < 1$.

Citation: Kerem Uǧurlu. Continuity of cost functional and optimal feedback controls for the stochastic Navier Stokes equation in 2D. Communications on Pure & Applied Analysis, 2017, 16 (1) : 189-208. doi: 10.3934/cpaa.2017009
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