Title page for ETD etd-11112009-200229

Type of Document Dissertation
Author Fang, Liqun
Author's Email Address liqun_fang@yahoo.com
URN etd-11112009-200229
Title Stochastic Navier-Stokes Equations with Fractional Brownian Motions
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Sundar, Padmanabhan Committee Chair
Cochran, George W. Committee Member
Kuo, Hui-Hsiung Committee Member
Lawson, Jimmie Committee Member
Perlis, Robert Committee Member
Frank, Juhan Dean's Representative
  • stochastic integration
  • bounded
  • boundary condition
  • mild solution
  • stochastic process
  • Hodge-Leray projection
  • martingale
  • weak convergence
Date of Defense 2009-07-28
Availability unrestricted
The aim of this dissertation is to study stochastic Navier-Stokes equations with a fractional Brownian motion noise. The second chapter will introduce the background results on fractional Brownian motions and some of their properties. The third chapter will focus on the Stokes operator and the semigroup generated by this operator. The Navier-Stokes equations and the evolution equation setup will be described in the next chapter. The main goal is to prove the existence and uniqueness of solutions for the stochastic Navier-Stokes equations with a fractional Brownian motion noise under suitable conditions. The proof is given with full details for two separate cases based on the value of the Hurst parameter H: 1/2 < 1 and 1/8 < 1/2.
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