Date of Award
Doctor of Philosophy
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.
Ming, Ju, "Optimal control of stochastic flow" (2009). Graduate Theses and Dissertations. 10782.