2D Navier-Stokes equation with cylindrical fractional Brownian noise

TL;DR

This paper investigates the 2D Navier-Stokes equation with cylindrical fractional Brownian noise, establishing local and global existence and uniqueness results depending on the Hurst parameter range.

Contribution

It extends previous work by proving existence and uniqueness for a broader range of Hurst parameters in stochastic 2D Navier-Stokes equations.

Findings

Local existence and uniqueness for 7/16<H<1/2

Global existence and uniqueness for 1/2<H<1

Extension of results beyond the H=1/2 case

Abstract

We consider the Navier-Stokes equation on the 2D torus, with a stochastic forcing term which is a cylindrical fractional Wiener noise of Hurst parameter $H$. Following [3,8] which dealt with the case $1/2$, we prove a local existence and uniqueness result when $7/16< H< 1/ 2$ and a global existence and uniqueness result when $ 1/2<H<1$.