  In this article, we study optimal feedback control synthesis of stochastic 2D
Navier-Stokes equations perturbed Levy type noise with distributed stochastic
control process acting on the state equation. We use the dynamic programming
approach to solve this control problem which involves the study of second order
infinite dimensional Hamilton- Jacobi-Bellman (HJB) equation consisting of an
integro-differential operator with Levy measure associated with the stochastic
control problem. Using the regularizing properties of the transition semigroup
corresponding to the stochastic 2D Navier-Stokes equation, we obtain a smooth
solution in weighted function space for the HJB equation and solve the
resultant feedback control problem.
