Degree Type

Dissertation

Date of Award

2009

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Lisheng Hou

Abstract

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.

Copyright Owner

Ju Ming

Language

en

Date Available

2012-04-30

File Format

application/pdf

File Size

87 pages

Included in

Mathematics Commons

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