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On the Dynamic Programming Approach for the 3 D Navier–Stokes Equations

On the Dynamic Programming Approach for the 3 D Navier–Stokes Equations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

On the Dynamic Programming Approach for the 3 D Navier–Stokes Equations

Applied Mathematics and Optimization , Volume 57 (3) – Jun 1, 2008

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References (21)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-007-9024-7
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2008

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