Applied Mathematics and Optimization, Vol.57, No.3, 329-348, 2008
On the dynamic programming approach for the 3D Navier-Stokes equations
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.