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

Kerem Uǧurlu

doi:10.3934/cpaa.2017009

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2017, Volume 16, Issue 1: 189-208. Doi: 10.3934/cpaa.2017009

This issue Previous Article Resonant problems for fractional Laplacian Next Article Zero dissipation limit to rarefaction wave with vacuum for a one-dimensional compressible non-Newtonian fluid

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

Kerem Uǧurlu

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

Author Bio: E-mail address: kugurlu@usc.edu

Received: February 29, 2016

Revised: June 30, 2016

Published: January 2018

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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 $0 < \epsilon < 1$.

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Mathematics Subject Classification: 60H15, 60H30.

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