Optimal control of stochastic flow

In this dissertation, we consider the optimal control problems of stochastic Burgers equations (SBEs) and stochastic Navier-Stokes equations (SNEs) . We first study the Wick type SBEs and SNEs with additive white noise, a Wiener chaos expansion of the optimal solution is derived. Furthermore, we apply polynomial chaos expansion to study stochastic flow control problem, particularly, vorticiy reduction by a stochastic boundary action in backward facing step channel . In these three optimal control problems, variational formulations are developed. Numerical results by using the finite difference method and the finite element method are presented to validate our methodology