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The approximation of the value function associated to a stabilization problemformulated as optimal control problem for the Navier-Stokes equations indimension three by means of solutions to generalized Lyapunov equations isproposed and analyzed. The specificity, that the value function is notdifferentiable on the state space must be overcome. For this purpose a newclass of generalized Lyapunov equations is introduced. Existence of uniquesolutions to these equations is demonstrated. They provide the basis forfeedback operators, which approximate the value function, the optimal statesand controls, up to arbitrary order.

Feedback Stabilization of the Three-Dimensional Navier-Stokes Equations using Generalized Lyapunov Equations