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The dynamic programming approach for the control of a 3 D flow governed by the stochastic Navier–Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton–Jacobi–Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2008
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