On the dynamic programming approach for the 3D Navier-Stokes equations

Details On the dynamic programming approach for the 3D Navier-Stokes equations On the dynamic programming approach for the 3D Navier-Stokes equations

2006-09-14

arxiv.org/abs/math/0609389v1

Mathematics

Optimization and Control

18 pages

Scientific paper

The dynamic programming approach for the control of a 3D 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.

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