Doctor of Philosophy (PhD)
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.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Fang, Liqun, "Stochastic Navier-Stokes equations with fractional Brownian motions" (2009). LSU Doctoral Dissertations. 1680.