A Stochastic Maximum Principle for Control Problems Constrained by the Stochastic Navier-Stokes Equations

Peter Benner; Christoph Trautwein

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arXiv · 1810.12119

A Stochastic Maximum Principle for Control Problems Constrained by the Stochastic Navier-Stokes Equations

Peter Benner·Christoph Trautwein

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Abstract

We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a necessary optimality condition to design the optimal control based on an adjoint equation, which is given by a backward SPDE. Moreover, we show that the optimal control satisfies a sufficient optimality condition. As a consequence, we can solve uniquely control problems constrained by the stochastic Navier-Stokes equations especially for two-dimensional as well as for three-dimensional domains.

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BibTeX RIS

Peter Benner, Christoph Trautwein. 2018-10-26. A Stochastic Maximum Principle for Control Problems Constrained by the Stochastic Navier-Stokes Equations. https://arxiv.org/abs/1810.12119

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